Question

Which of the following pairs of functions are inverses of each other?

Answer 1

Answer:

Step-by-step explanation:

Rearrange each function to solve for x.

Switch x and y,

The resulting equation is the inverse function.

A:

f(x) = y = 5+x

x = y-5

y = x-5

f⁻¹(x) = x-5

g(x) = 5-x ≠ f⁻¹(x)

g(x) is not the inverse of f(x).

:::::

B:

f(x) = y = 2x-9

x = (y+9)/2

y = (x+9)/2

f⁻¹(x) = (x+9)/2

g(x) = (x+9)/2 = f⁻¹(x)

g(x) is the inverse of f(x).

:::::

C:

f(x) = y = 2/x - 6

x = 2/(y+6)

y = 2/(x+6)

f⁻¹(x) = 2/(x+6)

g(x) = (x+6)/2 ≠ f⁻¹(x)

:::::

D:

f(x) = y = x/3 + 4

x = 3y - 12

y = 3x - 12

f⁻¹(x) = 3x - 12

g(x) = 3x - 4 ≠ f⁻¹(x)

g(x) is not the inverse of f(x).