Question

Question #40cbb

Answer 1

The domain is `x>0`

Explanation:

The domain of `g^(-1)(x)` is the range of `g(x)`, and the range of `g^-1(x)` is the domain of `g(x)`.

This is because `g^-1(x)` is a reflection of `g(x)` in the line `y=x`, so all the `x` coordinates switch to be the `y` coordinates, and the `y` coordinates become the `x` coordinates (e.g. if a point on `g(x)` is `(2,4)`, this would translate to `(4,2)` on `g^-1(x)`). Hence the range and domain would also switch around.