Chapter 1.6, Problem 138E

To determine

ToFind: whether the given two functions in each graph is inverse of each other and explain with reasoning.

Answer to Problem 138E

two functions in graph (a) are not inverse of each other.

Explanation of Solution

Given

Graphs are given below.

  

Calculation:

Since, graph of a function and its inverse function is a reflection or mirror image in the line $y=x$ which passes through origin.

For example, functions $f\left(x\right)=3-4x$ and $g\left(x\right)=\frac{3-x}{4}$ are inverse of each other as shown in the graph below.

Its graphs mare plotted using coordinates given below.

Plotting $f\left(x\right)=3-4x$ for the coordinates.

  $\begin{array}{cc}x& y\\ 0& 3\\ \frac{3}{4}& 0\end{array}$

Plotting $g\left(x\right)=\frac{3-x}{4}$ for the coordinates.

  $\begin{array}{cc}x& y\\ 0& \frac{3}{4}\\ 3& 0\end{array}$

  

Here, it can be seen that both the functions are reflection of each the in the line $y=x$ .

In graph (b), (c) and (d), both functions are reflection of each other in line $y=x$ whereas in graph (a) both functions are not reflections.

Therefore, two functions in graph (a) are not inverse of each other.