Question

4. Determine whether f(x) = 1/3x + 5 and g(x) = 3x - 15 are inverse functions.

Answer 1

Answer:

YES! we conclude that f(x) = 1/3x + 5 and g(x) = 3x - 15 are inverse functions.

Step-by-step explanation:

Given

Given that the function f(x) and g(x) are inverse functions.

$f\left(x\right)\:=\:\frac{1}{3}x\:+\:5$

$g(x) = 3x - 15$

To determine

Let us determine whether f(x) = 1/3x + 5 and g(x) = 3x - 15 are inverse functions.

Determining the inverse function of f(x)

A function g is the inverse function of f if for y = f(x), x = g(y)

$y=\frac{1}{3}x+5$

Replace x with y

$x=\frac{1}{3}y+5$

Solve for y

$y=3x-15$

Therefore,

YES! we conclude that f(x) = 1/3x + 5 and g(x) = 3x - 15 are inverse functions.