Will give 50 pts
another question is

which pairs of functions are inverse of each other? choose all that is correct

a. f(x) = 2x + 3 and g(x) = 0.5x - 3

b. f(x) = 1/6x - 2 and g(x) = 6x -12

c. f(x) = 1/3x + 5 and g(x) = 3x - 15

d. f(x) = x^2 +7 and g(x) = + or - squared x-7

C. f(x) = 1/3x + 5 and g(x) = 3x - 15

f^-1(21) = 5

Step-by-step explanation:

To find the inverse. we exchange x and y and then solve for y

A. f(x) = 2x + 3 and g(x) = 0.5x - 3

y = 2x+3

x = 2y+3

x-3 = 2y

(x-3)/2 =y

This is not g(x)

B. f(x) = 1/6x - 2 and g(x) = 6x -12

y = 1/6 x -2

x = 1/6 y -2

x+2 = 1/6 y

6x +12 =y

This is not g(x)

C. f(x) = 1/3x + 5 and g(x) = 3x - 15

y = 1/3 x+5

x = 1/3 y +5

x-5 = 1/3 y

3x-15 =y

This is g(x) so it is the inverse

D. f(x) = x^2 +7 and g(x) = + or - squared x-7

y = x^2 +7

x = y^2 +7

x-7 = y^2

±sqrt(x-7) = y

This is not g(x)

3.  f^-1 (21) = ?

f(x) = 2x+11

The functions are inverses so the input of 1 is the output of the other

f(a) = b means f^-1 (b) = a

We want to know when y =21

21 = 2x+11

Subtract 11 from each side

21-11 = 2x+11-1

10 = 2x

Divide by 2

10/2 = 2x/2

5 =x

f^-1(21) = 5

yes the total will be same because in both of them the expression.is rearranged but their sign remains the same hence it hss just been shuffled

step-by-step explanation: