Question

How do you determine whether the function `f(x)=3x+5` has an inverse and if it does, how do you find the inverse function?

Answer 1

First, we have to determine if `f` is a one-to-one or many-to-one. Only one-to-one functions have inverse functions, while many-to-one functions have inverse mappings.

In order to find the inverse of `f(x)`, we must find `f(y)` and then apply this transformation: `y=x`.

Let `y=f(x)`

`y=3x+5`

`3x=y-5`

`x=f(y)=1/3(y-5)`

`f^-1(x)=y=1/3(x-5)`