Question

If f(x) = 5x, what is f–1(x)?

Answer 1

`{f}^( - 1) (x) = switching \: the \: x \: for \\ the \: y \\ f(x) = 5x - - > x = 5y \\ solve \: for \: y. \: {f}^( - 1) (x) = (x)/(5)`

Answer 2

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

Explanation:

`f^(-1)(x)` is the inverse function of
`f(x)`, that is, if
`f(x)` transform "a" to "b", then
`f^(-1)(x)` transform "b" to "a".

thus:

`f(x)= 5x\\\\y = 5x \ \ \ \ \ \ \ \ \ \ \ Making \ f(x)=y \\\\(y)/(5)= x \ \ \ \ \ \ \ \ \ \ \ divide \ both \ sides \ by \ 5\\\\x=(y)/(5) \\\\so \ f^(-1)(y) =(y)/(5)\\\\`

due to the choice of variable is arbitrary, we can write this like:

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