Question

Use compositions to determine if the functions below are inverses of

Answer 1

Answer:

They are not inverse functions

Step-by-step explanation:

Given

$f(x) = 5x$

$f^{-1}(x) = x$

Required

Determine if both are inverse functions

First calculate the inverse of f(x)

$f(x) = 5x$

Replace f(x) with y

$y = 5x$

Swap x and y

$x = 5y$

Make y the subject

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

Replace y with f-1(x)

$f^{-1}(x) = \frac{1}{5}x$

By comparison:

$f^{-1}(x) = x$ and $f^{-1}(x) = \frac{1}{5}x$ are not the same:

Hence:

$f(x) = 5x$ and $f^{-1}(x) = x$ are not inverse functions