Which pair of functions are inverses of each other?
Wanting to make sure of answers in this pretest
Answers
Answer:
The only pair of functions that are inverses of each other are the ones for option D.
Step-by-step explanation:
Two functions, f(x) and g(x), are inverses if and only if:
f( g(x) ) = x
g( f(x) ) = x
So we need to check that with all the given options.
A)
[tex]f(x) = \frac{x}{7} + 10 \\g(x) = 7*x - 10\\[/tex]
then:
[tex]f(g(x)) = \frac{7*x + 10}{7} -10 = x + \frac{10}{7} - 10[/tex]
This is clearly different than x, so f(x) and g(x) are not inverses.
B)
[tex]f(x) = \sqrt[3]{11*x} \\g(x) = (\frac{x}{11} )^3[/tex]
Then:
[tex]f(g(x)) = \sqrt[3]{11*(\frac{x}{11})^3 } = \sqrt[3]{\frac{x^3}{11^2} } = \frac{x}{11^{2/3}}[/tex]
This is different than x, so f(x) and g(x) are not inverses.
C)
[tex]f(x) = \frac{7}{x} -2 \\g(x) = \frac{x + 2}{7}[/tex]
Then:
[tex]f(g(x)) = \frac{7}{\frac{x + 2}{7} } - 2 = \frac{7*7}{x + 2} - 2[/tex]
Obviously, this is different than x, so f(x) and g(x) are not inverses.
D)
[tex]f(x) = 9*x - 6\\g(x) = \frac{x + 6}{9}[/tex]
Then:
[tex]f(g(x)) = 9*\frac{x + 6}{9} - 6 = x + 6 - 6 = x\\g(f(x)) = \frac{(9*x - 6) + 6}{9} = x[/tex]
In this case we can conclude that f(x) and g(x) are inverses of each other.
Related Questions
find rational numbers between
( -7 and 1/3)
5/9 and 2/3
[tex] \frac{ - 2}{5} and \frac{ - 3}{7} [/tex]
Answers
Answer:
i know there's a lot of explanation. but it helps u for sure :)
Step-by-step explanation:
1)
[tex]-7 \ and \ \frac{1}{3} = \frac{-7}{1} \ and \ \frac{1}{3}\\\\LCM \ of \ 1 \ and\ 3 = 3\\\\\frac{-21}{3} \ and \ \frac{1}{3}\\\\To \ find \ rational \ numbers \ between \ \frac{-21}{3} \ and \ \frac{1}{3} \ write \ any \ number \ between \ -21 \ and \ 1 \ with \ denominator \ 3. \\\\That \ is, \ \frac{-20}{3}, \frac{-19}{3}, \frac{-18}{3}.....[/tex]
2)
[tex]\frac{5}{9} \ and \ \frac{2}{3}\\\\Similarly \ take \ LCM \ of \ 9 \ and \ 3 = 9\\\\Since \ it \ is \ still \ complicated \ to \ find \ rational \ number \ between \ \frac{5}{9} \ and \ \frac{6}{9},[/tex]
[tex]because \ there \ exists \ no\ natural \ number \ between \ 5 \ and \ 6.[/tex]
[tex]We \ will \ multiply \ numerator \ and \ denominator\ by\ 10. \\\\Therefore\ \frac{5}{9} \ and \ \frac{6}{9} \ becomes \ \frac{50}{90} \ and \ \frac{60}{90}.[/tex]
[tex]Keeping \ denominator \ 90 \ write \ numbers \ from \ 50 \ to \ 60 \ in \ the\ numerator.\\\\That \ is , \frac{51}{90}, \frac{52}{90}, \frac{53}{90}, \frac{54}{90}, .\ .\ .[/tex]
3)
[tex]LCM \ of \ 5 \ and \ 7 = 35\\\\\frac{-2}{5} \ and \ \frac{-3}{7}\ becomes \ \frac{-14}{35} \ and \ \frac{-15}{35}\\\\Now \ multiply \ denominator \ and \ numerator \ by \ 10\\\\\frac{-140}{350} \ and \ \frac{-150}{350}.\\\\Rational \ numbers \ are \frac{-141}{350}, \frac{-142}{350}, \frac{-143}{350}, . \ . \ . \[/tex]
Tip :
1. Make the denominator same.
2. Multiply numerator and denominator by 10 , 100 or 1000
3. Just write the natural numbers between the 2 numerators keeping denominator same.
1) Which triangle is both scalene and acute?
70°
510
10 ft
6.8 ft
10 ft
9 Ft
40°
70°
58° 71°
8.3 ft
10 ft
10 ft
102
90°
7 ft
10 ft
7 ft
31°
47°
35°
55°
13.3 Ft
12.2 ft
Done
Answers
Answer:
Step-by-step explanation:
Top right one. All angles are acute( < 90 degrees) and different .
Suppose the salaries of university professors are approximately normally distributed with a mean of $65,000 and a standard deviation of $7,000. If a random sample of size 25 is taken and the mean is calculated, what is the probability that the mean value will be between $62,500 and $64,000? a. .1465 b. .0827 c. .0371 d. .2005
Answers
Answer:
0.2005
Step-by-step explanation:
Mean, m = 65000
Standard deviation, σ= 7000
Sample size, n = 25
Let X = random variable of salary
Recall:
Z = (μ - x) /(σ/√n)
P(62500 ≤ x ≤ 64000) =?
Pr((65000 - 62500)/7000/√25 ≤ z ≤ (65000 - 64000) / 7000/√25)
P(2500 / 1400 ≤ z ≤ 1000/1400)
P = (1.79 ≤ z ≤ 0.714)
Using the normal distribution table or a Z probability calculator
0.4633 - 0.2624
= 0.2009
Kelly is making a quilt out or "3 square yards of white fabric and 's square yards of yellow fabric. What is the unit rate of yellow
fabric to white fabric?
СА.
3 square yards of yellow fabric to 1 square yard of white fabric
Ов
of a square yard of yellow fabric to 1 square yard of white fabric
OC
of a square yard of yellow fabric to 1 square yard of white fabric
OD
square yards of yellow fabric to 1 square yard of white fabric
Answers
Answer:
c
Step-by-step explanation:
I think it is c
At the neighborhood block party, Hassan served 3 gallons of hot chocolate and 1/2 of a gallon of apple cider. How much more hot chocolate than apple cider did Hassan serve?
Write your answer as a fraction or as a whole or mixed number.
Answers
Answer:
2 gallons and 1/2
Step-by-step explanation:
You just have to subtract 1/2 from 3.
3 - 1/2 = 2 1/2
or
3 - .5 = 2.5
And 2 1/2 is how much more he served.
Answer: 5 times more hot chocolate
Step-by-step explanation:
On average, there are 177,000 cars on the road every hour in Los Angeles. 1 point
In March 2020, the coronavirus shutdown, resulted in Los Angeles having
80% fewer cars on the road. How many cars were on the road in March
2020 every hour in Los Angeles, after the 80% reduction?
Answers
Answer:
Number of cars on road in 2020 = 35,400 car
Step-by-step explanation:
Given;
Number of cars on road = 177,000
Decrease in cars on road in 2020 = 80%
Find:
Number of cars on road in 2020
Computation:
Number of cars on road in 2020 = Number of cars on road[1 - Decrease in cars on road in 2020]
Number of cars on road in 2020 = 177,000[1-80%]
Number of cars on road in 2020 = 177,000[1-0.80]
Number of cars on road in 2020 = 177,000[0.20]
Number of cars on road in 2020 = 35,400 car
W varies directly with the square of n and when n = 3, W = 117. Find n when W = 637
n =
Answers
Answer:
n = 7
Step-by-step explanation:
Varies directly
w/n² = k
---------------------------
when n = 3, W = 117
k =117/3²
k = 117/9
k = 13
-------------------------
Find n when W = 637
637/n² = 13
637 /13 = n²
49 = n²
7 = n
Which pair of ratios form a proportion? A. 2 : 3 and 3 : 4 B. 8 : 12 and 16 : 20 C. 4 : 7 and 12 : 21 D. 9 : 15 and 10 : 16
Answers
Answer:
C 4:7 and 12:21
Step-by-step explanation:
4×3 => 12
7×3 => 21
Segment CB is a____
Answers
Answer:
Radius
Step-by-step explanation:
CB = AB/2
Since AB is the diameter, CB is a radius
alice does a sponsored walk se starts from home on monday 8am she arrives back home 55 hours later work out when she arrives back home
Answers
Answer: Alice returns on Wednesday, 3 pm.
Step-by-step explanation: One day is 24 hours long. 55 hours is 2 days and 7 hours. So Alice comes back home on Wed , add 8 am 7 hours and you get 3 pm
The time that Alice would arrive home from the sponsored walk given the the time she starts the walk is Wednesday by 3pm.
What time would Alice arrive home?The first step is to divide 55 hours into days. This can be done by dividing 55 hours by 24.
55/24 = 2 days 7 hours
The second step is to add 2 days 7 hours to 8am: Monday 8am + 2 days 7 hours = Wednesday 3pm
To learn more about how to calculate time, please check: https://brainly.com/question/26290873
a baker made cakes, cookies, and buns, of the total number of baked products he made, 28% more cookies. The number of cakes was three times the number of buns. He made 270 cakes. He sold 40 buns and 120 cakes. how many cookies must he sell that The ratio of the number of buns left the number of cakes to the number of cookies left is 1 : 3 : 2. HELP PLEASEEE
Answers
Answer:
40 cookies was sold
Step-by-step explanation:
Let x represent the number of cakes baked, y represent the number of cookie baked and z represent the number of buns baked.
He made 270 cakes. Therefore x = 270
28% of the total baked products where cookies, hence:
0.28(270 + y + z) = y
75.6 + 0.28z = 0.72y
0.72y - 0.28z = 75.6 (1)
The number of cakes was three times the number of buns. Hence:
x = 3z
3z = 270
z = 90
Put z = 90 in equation 1:
0.72y - 0.28(90) = 75.6
0.72y -25.2 = 75.6
y = 140
Therefore 270 cakes was baked, 140 cookies was baked and 90 buns was baked.
He sold 40 buns and 120 cakes, the number of buns and cakes left is 50 buns and 150 cakes. Let us assume that number of cookies left was a. Since the ratio of left buns to cakes to cookies is 1:3:2. Hence:
(1/6) * (50 + 150 + a) = 50
300 = 200 + a
a = 100
Therefore 100 cookies was left. The number of sold cookies = 140 - 100 = 40
easy question for alot points
Answers
multiply 3.28 by 2
=6.56ft
Answer:
B) 2meter line segment
Step-by-step explanation:
3.28ft=1m
Then an easy way to find the answer is to multiply 3.28 by 2
to if the 6.3ft line is under or over 2m
3.28 multiplied by 2 equals 6.56
6.56>6.3
therefore, the 6.3ft. line segment is just a little shorter than 2m
How can a group of people be considered a population and sample?
Answers
The entire group about which you want to draw conclusions is referred to as a population. A sample is a subset of the population from which you will collect data. The sample size is always smaller than the population's total size. A population in research does not always refer to people.
Find the area of the shaded regions. Give your answer as a completely simplified exact value in terms of pi (no approximations)
Answers
Answer:
40π in^2
Step-by-step explanation:
360°/72°=5
so, each of the two shaded regions are 1/5 of the circle.
the formula for finding the area of a circle is πr^2, so:
area for one of the shaded regions:
1/5πr^2
1/5π(10)^2
1/5π100
20π in^2
this means that the area for one of the shaded regions is 20π. however, since there are two of them:
2(20π)=40π
so, the area of the shaded regions is 40πin^2
Can somebody please tell me the answer of this?
Answers
Answer:
20
Step-by-step explanation:
[tex]15^2+b^2=25^2\\225+b^2=625\\625-225=b^2\\b^2=400\\\sqrt{400}=20[/tex]
if 5,4 and 15 and x are in proportion find the value of x
Answers
15/5 = 3
4 x 3 = 12
Which is proportional.
Marci performed a division. 175 was the dividend, 5 was the divisor, and 35 was the quotient. Which is a correct representation of this problem
Answers
Answer:
175/5 = 35
Step-by-step explanation:
dividend/divisor = quotient
175/5 = 35
Consider the sequence 3/4,4/5,5/6,6/7,... Which statement describes the sequence? The sequence diverges. The sequence converges to 1. The sequence converges to [infinity]. The sequence converges to –[infinity].
Answers
Answer:
The sequence converges to 1.
Step-by-step explanation:
[tex]\frac{3}{4}, \frac{4}{5}, \frac{5}{6}, \frac{6}{7}\\\\The \ general \ term = \frac{n -1}{n}\\\\ \lim_{n \to \infty} (\frac{n -1}{n}) = \lim_{n \to \infty} \frac{n(1 -\frac{1}{n})}{n} = \lim_{n \to \infty} 1 - \frac{1}{n} = 1 - \lim_{n \to \infty} \frac{1}{n} = 1[/tex]
[tex][ \lim_{n \to \infty} \frac{1}{n} = 0][/tex]
how to do u write 10*10*10*10*10 as word form
Answers
Answer:
One hundred thousand
Step-by-step explanation:
It would be one hundred thousand because 10*10*10*10*10 is 100,000, hence 100,000 would be, well, one hundred thousand.
Answer:
ten times ten times ten times ten times ten or one hundred thousand
Step-by-step explanation:
PLZ HELP ASAP!!! What is the area of sector DEF in terms of pi ?
120°
3 cm
E
Answers
Answer:
Area of the sector : D.
3π cm²
AABC - DEF. What sequence of transformations will move A ABC onto A DEF? 10 8 A(0.4) B(0,0) C(3.0) -10 -8 -6 -4:1-2 6 8 10 -2D(0.2) 24 8 -10 E(0.-10) F( 6-10)
Answers
Answer:
Option B
Step-by-step explanation:
It's clear from the graph attached,
ΔABC has been dilated and shifted downwards.
Length of segment AB = 2 units
Length of segment DE = 4 units
Scale factor by which the dilation has been done = [tex]\frac{\text{Dimension of the image triangle}}{\text{Dimension of the original triangle}}[/tex]
Scale factor = [tex]\frac{DE}{AB}[/tex]
= [tex]\frac{4}{2}[/tex]
= 2
Therefore, triangle ABC is dilated by a scale factor of 2 about the origin.
Lets consider a point B(0, 0) from the given graph and analyze the transformations done.
If a point B(0, 0) is shifted to point E(0, -10) which follows the rule,
B(0, 0) → E(0 + h, 0 + k)
Here, 'h' and 'k' are the translations of the given point over x-axis and y-axis.
Therefore, (0 + h) = 0 ⇒ h = 0
0 + k = -10
k = -10
Hence, triangle ABC has been dilated by a scale factor of 2 centered at origin and followed by the translation (x, y - 10)
Option B is the correct option.
What is the result of adding two or more numbers?
Answers
Answer: A sum
Step-by-step explanation: The result of adding two or more numbers together is a sum.
When two (or more) numbers are added together, the result is called a sum.
SOMEONE HELP PLEASE!!!
Answers
Answer:
0=0 1=1 2=0 3=0 4=1 5=3 6=1 7=0 8=0 9=1 10=2 11=1 12=2 13=0 14=0 15=3 16=0
Step-by-step explanation:
There was no question so here above is the Dollars spent graph in numbers not dots!
I did this question (5 a) on sketching transformations, but when I graphed it it was incorrect. What did I do wrong?
Answers
- 3 is for vertical displacement sis.
( Sorry about my bad graphing and bad quality of the pic )
Determine the area of the figure shown. Note that each square unit is one unite in length
Answers
Answer:
74 units squared
Step-by-step explanation:
we know that the area of a square or rectangle is A = L × w
so we should just separate the object into it's individual rectangles/squares, solve for their areas, then add them together.
so I'll start with the middle square its length is 8 and width is 8 too.
A = 8 × 8
A = 64
now we'll move on to the other small ones to the side.
the one on the right side it's length is 2 and width is 2.
A = 2 × 2
A = 4
and then the last one on the left, Length is 3, width is 2.
A = 2 × 3
A = 6
now we'll add up all of the areas to get the total area.
Total = 64 + 4 + 6
Total = 74 units squared
Help- No links please!!
Answers
Answer:
2 times length of AB
Step-by-step explanation:
Given
[tex]AB =50\%[/tex]
Required
Length of line with 100%
To get the length of line segment that is 100%, simply multiply AB by 2
i.e.
[tex]2 * AB =2 * 50\%[/tex]
[tex]2 AB =100\%[/tex]
Assume AB = 5cm (at 50%). The length at 100% will be 10cm i.e. 2 * 5cm
Write the inverse function for the function, ƒ(x) = 1/2 x + 4. Then, find the value of ƒ -1(4). Type your answers in the box.
ƒ -1(x) =
ƒ -1(4) =
Answers
Answer:
[tex] {f}^{ - 1} (x) = 2x - 8[/tex]
[tex] {f}^{ - 1} (4) = 0[/tex]
Step-by-step explanation:
[tex] y = \frac{1}{2} x + 4 = = = > \\y - 4 = \frac{1}{2} x = = = > \\ 2y - 8 = x = = > {f}^{ - 1} (x) = 2x - 8[/tex]
[tex] \frac{1}{2} x + 4 = 4 = = = > \\ \frac{1}{2} x = 0 = = = > x = 0[/tex]
plzz help asap ill give brainliest
Answers
Answer:
[tex]c=\frac{ab}{a+b}[/tex]
Step-by-step explanation:
To solve for [tex]c[/tex], our goal is to isolate it.
Start by multiply both sides by [tex]ab[/tex]. That way, we'll still have only one term with [tex]c[/tex], but we'll be able to get rid of two messy fractions.
[tex]b+a=\frac{ab}{c}[/tex]
Taking the reciprocal of both sides:
[tex]\frac{1}{a+b}=\frac{c}{ab},\\c=\boxed{\frac{ab}{a+b}}[/tex]
*Note: You cannot take the reciprocal of both sides if you're adding fractions. This is why we can't just take the reciprocal of both sides in the initial equation.
Alternate solution:
[tex]\frac{1}{a}+\frac{1}{b}=\frac{b}{ab}+\frac{a}{ab}=\frac{1}{c},\\\\\frac{b+a}{ab}=\frac{1}{c},\\\\c=\frac{ab}{b+a}=\boxed{\frac{ab}{a+b}}[/tex]
Answer:
c=ab
a+b
Step-by-step explanation:
1 + 1= 1
a. b. c
a+b = c
ab
a+b= ab
c
ac+bc=ab
c(a+b)=ab
c(a+b)=ab
a+b. a+b
c=ab
a+b
which pair of expressions are equivalent?
A. j + j + j + j and j4
B. 16g + 10 - 4g and 20g + 10
C. 16c + 24c and (4c + 6c)
D. 14e^2 + 3e + 8 and 17e^2 + 8
Answers
Answer:
A.
[tex]j + j + j + j \: and \: j4[/tex]
SOMEONE HELPPP PLEASE!! Complete the table to represent the number of seashells in the collection after the first four summers
Answers
Answer:
6 number of seashells for 1 Summer. 21 number of seashells for two summers. 36 number of seashells for three summers. 51 number of seashells for 4 summers.
Step-by-step explanation:
15 substituted in for f and x is the the number of summers.
Answer:
6
21
36
51
Illuminate test.