Chapter 1, Problem 101CR

To determine

To Graph the function and use the Horizontal Line Test to determine whether the function has an inverse function or not.

Explanation of Solution

Given:

The function is $h(t)={(t+5)}^{\frac{2}{3}}$

Approach:

1. Draw the given equations on the graph.
2. Draw the horizontal line parallel to the x-axis.
3. To determine horizontal line cutting the graph exactly one point.

Calculation:

Consider, $h(t)={(t+5)}^{\frac{2}{3}}$

The graph of the above equations is given below,

  

The horizontal line intersects the graph of a function in all places at exactly two points.

Then the given function should have not an inverse that is also a function.

So, we say this function does not pass the Horizontal Line Test.

Therefore, the function has not an inverse function.