Chapter 6.2, Problem 44PPS

To determine

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

Answer to Problem 44PPS

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

Explanation of Solution

Given Information:

Given function is :

  $g(x)=x^4-6x^2+1$

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 :

  

  $\begin{array}{l}\text{Clearly, from the graph , the horizontal line y= -3 intersects the graph }\\ \text{of the given function at four points }\text{.}\\ \text{So, the horizontal line cuts the graph of the given function at more than }\\ \text{1 point}\text{.}\\ \text{Hence, by the horizontal line test , the inverse of the given function}\\ \text{is not a function }\text{.}\end{array}$