Question

Determine the domain and range of f ^ - 1 * (x) given f(x) = 3 ^ (2x - 1) - 2

Answer 1

The graph of the function f(x) is shown below:

From it we notice that:

`\begin{gathered} \text{domf}=(-\infty,\infty) \\ \text{rangef}=(-2,\infty) \end{gathered}`

To determine the domain and range of the inverse function we just need to remember that the domain of the inverse is equal to the range of the original function; similarly, the range of the inverse is equal to the domain of the original function, therefore we have that:

`\begin{gathered} \text{domf}^(-1)=(-2,\infty) \\ \text{rangef}^(-1)=(-\infty,\infty) \end{gathered}`

and the answer is the third option.