Chapter 6, Problem 25SGR

To determine

Whether the inverse of the given function is also a function or not , using the horizontal line test.

Answer to Problem 25SGR

Yes, the inverse of the given function is a function.

Explanation of Solution

Given Information:

Given function is :

  $f(x)=x^3-3$

Concept Used:

The horizontal line test states that if the graph of a function $y=f(x)$ is such that no horizontal line intersects the graph in more than one point, then the function has an inverse function , or the inverse of the function $y=f(x)$ is a function.

Calculation:

The graph of the given function is :

  

  $\begin{array}{l}\text{Clearly, from the graph , any horizontal line intersects the graph }\\ \text{only at one point}\text{.}\\ \text{So, there is no horizontal line that intersects the graph at more than }\\ \text{one point}\text{.}\\ \text{Hence, by the horizontal line test , the inverse of the given function}\\ \text{is a function }\text{.}\end{array}$