Chapter 7.5, Problem 43E

To determine

To find: Whether the inverse of $f$ is a function and then find the inverse.

Answer to Problem 43E

The inverse of $f$ is not a function.

Explanation of Solution

Given:

The function is $f\left(x\right)=\frac{1}{x^2}+4$ .

Calculation:

Plot the graph of the function $f\left(x\right)=\frac{1}{x^2}+4$ as follows.

  

It is noticed that horizontal line intersects the graph more than once. So, there is no inverse of $f$ .