Chapter 6, Problem 26SGR

To determine

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

Answer to Problem 26SGR

No, the inverse of the given function is not a function.

Explanation of Solution

Given Information:

Given function is :

  $g(x)=-3x^4+2x-1$

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 :

  

  $\begin{array}{l}\text{Since the horizontal line y=1 intersects the graph at more than one point}\text{.}\\ \text{So, the function does not pass the horizontal line test}\text{.}\\ \text{Hence, by the horizontal line test , the inverse of the given function}\\ \text{is not a function }\text{.}\end{array}$