Question

The domain, range, and intercepts of a function are shown. Which set of information could be characteristics of the function's inverse?domain: x2-2y-intercept: (0,4)range: y2-1x-intercept: (8,0)

Answer 1

We have that given a function f(x) and its inverse f^(-1) (x), the next property is true:

"The range (domain) of a function f(x) is the domain(range) of the inverse function f^(-1) (x)"

Then, in this case, we have the following for the inverse function:

`\begin{gathered} \text{Domain:} \\ x\ge-1 \\ \text{Range:} \\ y\ge-2 \end{gathered}`

the intercepts with the axis will be the following:

`\begin{gathered} y-\text{intercept: (0,8)} \\ \\ x-\text{intercept: (4,0)} \end{gathered}`