Since f−1 undoes f, the domain of f−1 is all the possible values f could output, which is the range.

The range of f−1 is all the possible values that could have gone into f, which is the domain.

Hence

• the domain of f−1 is the range of f

• the range of f−1 is the domain of f

Example

Given f(x)=√4−x2​ find the domain and range of f−1.

First find the domain of f:

So the range of f−1 is −2≤f−1(x)≤2.

Then the range of f is

So the domain of f−1 is 0≤x≤2.