Chapter 5.2, Problem 99AYU

To determine

To find: The graph for this inverse of the given graph points, then find the similarities and the difference from the original graph.

Answer to Problem 99AYU

The graph for the inverse function with the dotted line is shown in Figure 2. The points for the given graph are reversed in the inverse graph but both the functions pass through the origin.

Explanation of Solution

Given:

The given points are $\left(-2,-3\right)$ , $\left(0,0\right)$ and $\left(1,5\right)$ .

Calculation:

Consider the given points are,

  $\left(-2,-3\right),\left(0,0\right),\left(1,5\right)$

The graph of the function $f\left(x\right)$ for the point $\left(x,y\right)$ , there is a symmetric graph for the points $\left(y,x\right)$ which will be on the graph of the function $f^{-1}\left(x\right)$ .

For the function $f^{-1}$ the inverse the points are,

  $\left(-3,-2\right),\left(0,0\right),\left(5,1\right)$

As the inverse and the original function are same, the graph and the function will coincide.

The graph for both the original and the inverse function is shown in Figure 1

  

Figure 1

The graph for the original function is shown with the straight line and the graph for inverse function is shown with the dotted line.

The graph for both the function passes through the origin. The points of the graph of inverse function is reversed from original function.