Question

Use compositions to determine if the functions below are inverses of

each other?*
f(x) = 5x & F-1(x) = x
Yes
No

Answer 1

They are not inverse functions

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 = (1)/(5)x`

Replace y with f-1(x)

`f^(-1)(x) = (1)/(5)x`

By comparison:

`f^(-1)(x) = x` and
`f^(-1)(x) = (1)/(5)x` are not the same:

Hence:

`f(x) = 5x` and
`f^(-1)(x) = x` are not inverse functions