Question

What is the inverse function of `f(x)=x+1` and how do you find `f^-1(2)`?

Answer 1

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

`f^(-1)(2) = 1`

Explanation:

`f^(-1)(x)` is a function such that `f(f^(-1))(x) = f^(-1)(f(x)) = x`

Then, if `y = f^(-1)(x)` we can apply `f(x)` to both sides to get

`f(y) = f(f^(-1)(x)) = x`

In the given function, this translates to

`y + 1 = x`

Then, as `y = f^(-1)(x)`, we can simply solve for `y` and substitute.

`y = x-1`

`=> f^(-1)(x) = x-1`

And so `f^(-1)(2) = 2-1 = 1`