Mathematics High School

For each pair of functions f and g below, find f(g(x)) and g(f(x)).
Then, determine whether f and g are inverses of each other.
Simplify your answers as much as possible.
(Assume that your expressions are defined for all x in the domain ofthe composition.
You do not have to indicate the domain.)

For Each Pair Of Functions F And G Below, Find F(g(x)) And G(f(x)).Then, Determine Whether F And G Are

Answers

Answer 1

Answer:

a)  f(g(x)) = [tex]\frac{1}{2(\frac{1}{2x} )}[/tex] = [tex]\frac{1}{\frac{1}{x} } }[/tex] = x

    g(f(x)) = [tex]\frac{1}{2(\frac{1}{2x} )}[/tex] = [tex]\frac{1}{\frac{1}{x} } }[/tex] = x

    f and g are inverses

b)   f(g(x)) = x + 3 + 3 = x + 6

     g(f(x)) = x + 3 + 3 = x + 6

     f and g are not inverses

Step-by-step explanation:

a)

f(g(x)) = [tex]\frac{1}{2(\frac{1}{2x} )}[/tex] = [tex]\frac{1}{\frac{1}{x} } }[/tex] = x

g(f(x)) = [tex]\frac{1}{2(\frac{1}{2x} )}[/tex] = [tex]\frac{1}{\frac{1}{x} } }[/tex] = x

Since f(g(x)) = g(f(x)) = x, then f and g are inverses

b)

f(g(x)) = x + 3 + 3 = x + 6

g(f(x)) = x + 3 + 3 = x + 6

Since f(g(x)) = g(f(x)) ≠ x, then f and g are not inverses

Related Questions

what power do I need to raise both sides of the following equation to? x^4=81

Answers

Answer:

Rise it to 2

( x ^2 ) ^2 − 9 ^2 = 0

Step-by-step explanation:

Please help.
Is algebra.

Answers

Answer:

B

Step-by-step explanation:

The first one is a binomial. It has two different terms on either side of the middle minus sign. y is raised to the 4 th power so that is degree 4. The answer is b

The second problem is ordered as 4 3 1 2

The powers determine the degree. The terms are all different and the number of terms is determined by the powers of the letters in the terms.

Answer:

Step-by-step explanation:

Find x and y
Show all the work

Answers

Answer:

x=27°

y=4 units

Step-by-step explanation:

To find x:

The sum of all the angles in a quadrilateral is 360°. In a rhombus (you know it's a rhombus because it's a quatrilateral where all the sides are congruent), opposite angles are congruent. Because you're given that the measure of ∠T is 127°, you also know that m∠V=127°. You also know that m∠U=m∠S=(2x-1)°.

Using this information, set up an equation.

127+127+(2x-1)+(2x-1)=360

You can just divide both sides by 2 to get:

127+(2x-1)=180

Then, just solve for x.

127+2x-1=180

2x+126=180

2x=54

x=27°

To find y:

All the sides are given to be congruent. That's what the little marks on the sides mean, and that's how we knew it was a rhombus earlier.

So SV=VU=UT=TS

SV=6y-5

VU=3y+7

Since SV=VU:

6y-5=3y+7

Solve for y.

3y=12

y=4

Hope I could help!

Mr. Davis is packing a box with books. The box is a rectangular prism with the 2 ft 3 ft 2 ft What is the volume of the box?

Answers

Answer:

12 ft^3

Step-by-step explanation:

Given data

Dimension

Lenght= 2ft

Width= 3ft

Height= 2ft

The expression for the volume is

Volume= L*W*H

Substitute

V= 2*3*2

V= 12 ft^3

Hence the volume of the box is 12 ft^3

Ryan invests $8,361 in a savings account with a fixed annual interest rate of 4.31% compounded monthly. After 10 years, what will be the balance in the account?

Answers

Answer:

12,750

Step-by-step explanation:

After investing for 10 years at 4.31% interest, your $8,361 investment will have grown to $12,750

Solve the equation: 5.4 -7.5 -6.3 = Solve the equation:​

Answers

The answer would be -8.4.

Answer:

[tex]5.4 - 7.5 - 6.3 = 5.4 - 13.8 \\ = - 8.4[/tex]

hey can you help me fast!!

Answers

Answer:

-10 / -2/5

Step-by-step explanation:

-10 / -2/5 = 25

25 is greater than 10

30 POINTSSSS ANSWER CORRECTLY THE LAST GUY TROLLED :/

Answers

Answer:

1.

A: Rectangular prism

B: Square pyramid

C: Triangular prism

2.

A: 82 square units

B: 48 square units

C: 48 square units (again)

Somehow Nets B & C have the same surface area.

Step-by-step explanation:

2A:

2(6 * 5) + 2(5) + 2(6)

2(30) + 10 + 12

60 + 22

82 square units

2B:

4((4 * 4)/2) + (4 * 4)

4(16/2) + 16

4(8) + 16

32 + 16

48 square units

2C:

2((3 * 4)/2) + (3 * 3) + (3 * 4) + (3 * 5)

2(12/2) + 9 + 12 + 15

12 + 9 + 27

12 + 36

48 square units

i have no idea what to do, someone pleasehelp.. please just give the straight forward equation and answer. thank you, 33 points to whoever does it

Answers

Answer:

Coordinates (1,6)

Equation x=1

Step-by-step explanation:

Center of highest point is 1 on the x and 6 on the y

Which pair of functions are inverses of each other?
Help help help!!!!!

Answers

Answer:

b

Step-by-step explanation:

check 1 by 1

a. [tex]y=\frac{\sqrt[3]{x}}{5}[/tex]

[tex]x=\frac{\sqrt[3]{y} }{5}[/tex]

125x^3=y which is not equal to g(x)

b. y=2x-9

inverse= x=2y-9

x+9=2y

y=(x+9)/2 which is equal to g(x). B is the answer.

Sam paid $8.28 for 18 stamps. At this rate, how much would it cost Sam to buy 12 stamps?

Answers

Answer: $5.52

Step-by-step explanation:

Given: Sam paid $8.28 for 18 stamps.

Thus, the cost of 18 stamps = $8.28

Then the cost of 1 stamp=

Thus, the cost of 1 stamp=$0.46

With the same rate , the cost of 12 stamps=

Therefore, the cost of 12 stamps= $5.52

hence, it costs $5.52 to Sam to buy 12 stamps.

8.28÷18 = 0.46

0.46 is the cost if 1 stamp

cost of 12 stamps= 0.46×12 = $5.52

happy to help :)

Find the value of x. Round to the nearest tenth.

Answers

Answer:

90 hope this helps

Step-by-step explanation:

If p=9 and q=30, evaluate the following expression:p−q/3​

Answers

Answer:

-1

Step-by-step explanation:

p = 9

q = 30

p - q/3

9 - 30/3

9 - 10

-1

Help please I’ll give brainliest

Answers

X=20 because 28/7 is 4 and 5*4 is 20
x=20 bc 7x4=28 therefor 5x4=20

plz plz plz plz help me on this question

Answers

9514 1404 393

Answer:

  C

Step-by-step explanation:

Solve for y to find the inverse:

  x = f(y)

  x = y/3 -2

  x +2 = y/3

  y = 3(x +2)

  f⁻¹(x) = 3(x +2) . . . . the inverse function

Cole wrote the number shown.

375,819

Lindsay used the same digits to write a number in which the value of the digit 7 is 110 of the value of the digit 7 in Cole’s number. Which number can be the one Lindsay wrote

Answers

the answer is the experience

A group of students is trying to determine the number of cars that move along a certain section of roadway. The dot plot below shows the speeds of 20 vehicles. Complete the table with the correct values from the dot plot.

Answers

Answer:# of cars: 1 | 0 | 0 | 0 | 2 | 4 | 5 | 3 | 0 | 2 | 2 | 1 |

Note: the answers are from left to right in order

Step-by-step explanation:

So this isn't as hard as it seems. You just count the X's and if there is like for example 1 x on 30 then the answer for 30 is 1 since there is only 1 X.

i can’t figure out the answer

Answers

Answer:

Pythagoras theorem

hypotenuse²=base²+height²

(24)²=base²+(9)²

576=base²+81

576-81=base²

494=base²

[tex] \sqrt{494} = base \\ 22.24 = base[/tex]

Cost of a puppy: $348.88
Discount: 23%

Answers

$ 268.6376 is the answer

I have no idea how to answer this question I've tried everything look at the Picture ​

Answers

Answer:

a. the error is that he wrote 0.05 instead of 0.2

0.148835 ≈ 0.2

b.

0.2 = 2 × 0.1

0.2 = 2 × 10⁻¹

The mass is about 2 × 10⁻¹ kg

Please help; I'll give brainliest for the first person who answers <3

Answers

Answer:

m puq

Step-by-step explanation:

Find the trigonometric ratios as simplified fractions and as decimals to the nearest thousandths (as necessary).



Sin X: Fraction_______ Decimal_______

Cos X: Fraction_______ Decimal______

Tan X: Fraction__________ Decimal______

Answers

Step-by-step explanation:

by using Pythagoras law

ZY=√{45²-27²)=36

sin X=ZY/XY=36/45=0.8

Cos X=XZ/XY=27/45=0.6

Tan X= YZ/XZ=36/27=1.33

Please help me out, thank you! I'll be giving brainliest and five stars to the correct answer!
Find the lowest value of the set of data this box-and-whisker plot represents. (Look at the image)

16
12
15
13

Also, please put an explanation to your answer, thanks :)

Answers

Answer:

Step-by-step explanation:

The lowest value of the set of data in the boxplot is 12.

12 is the lowest as:

15 is the lower quartile.

16 is the median.

18 is the upper quartile.

20 is the highest value.

The area of the rectangle below is 18 square units. What is the width of the rectangle? Write and solve a division equation to find the width of the rectangle.

Answers

Answer:

24/5 or 4 and 4/5

Step-by-step explanation:

3 and 3/4=15/4

18 divided by 15/4=4 and 4/5

4 and 4/5=24/5

24/5 times 15/4=18

Answer:

I agree with the person above but I'm not so sure.

Which category best describes the group of shapes

Answers

Answer:

Parallelograms

Step-by-step explanation:

Can someone help me on this plzzz

Answers

Answer:

b=15

How I got it:

32 + (7x4) = 32 + 28 = 60

60 divided by 4 = 15

Checking:

15 - 7 = 8

8 x 4 = 32

32 = 32

You can tell b = 15 is the correct answer.

Jack invested $2,900 in an account paying an interest rate of 8 % compounded
annually. Anthony invested $2,900 in an account paying an interest rate of 82%
compounded continuously. After 10 years, how much more money would Anthony
have in his account than Jack, to the nearest dollar?

Answers

Answer: $628

Step-by-step explanation:

Find the slope of the line through each pair of points using the formula.
(17, -19) (4, -15)

Answers

Answer:

-4/13

Step-by-step explanation:

(17 , -19)  ; (4 , -15)

Slope = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

          [tex]= \frac{-15-[-19]}{4-17}\\\\=\frac{-15+19}{4-17}\\\\=\frac{4}{-13}\\\\= \frac{-4}{13}[/tex]

Answer:

- 4 / 13

Step-by-step explanation:

Algebra work is easy :)

good luckkk

Vertical lines have _________ slope.

Answers

Try drawing a vertical line on a graph
The line would be going straight but unmoving
Slope = rate of change

Vertical lines have undefined slope

I thought I could do this myself but failed, can someone please help me answer this and show work so I can know what to do for future reference. I would like to complete this seeing how this is my last question of the week.

Answers

Answer:

area: 1070

perimeter: 434 units

Step-by-step explanation:

area:

- use pythagoream theorem to find the height, which is gonna be 84

- from there, you're gonna wanna find the area of the rectangle and then the two triangles. the way i do it is by just finding the area of the rectangle first, 100x84 = 8400, and then finding the area of the triangles (35x84/2 = 1470 and 20x84/2 = 840)

- you have the area of all shapes, now just add them together (8400+1470+840 = 10710)

perimeter:

just add all the lengths given together.

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