Chapter 4.7, Problem 33PPS

To determine

To write an equation for the inverse function $f^{-1}(x)$ that satisfies the given condition.

Answer to Problem 33PPS

Equation for the inverse function is $f^{-1}(x)=(3/2)x-12$ .

Explanation of Solution

Given information: Graph of $f(x)$ contains the points (-3,6) and (6,12).

Formula used:

The equation of a function passes through two points is,

  $y-y_1=\left[(y_2-y_1)/(x_2-x_1)\right](x-x_1)$ .

Calculation:

For finding the equation for the inverse function $f^{-1}(x)$ ,have to first find the equation of $f(x)$ .

The equation of a function passes through two points is,

  $\begin{array}{l}y-y_1=\left[(y_2-y_1)/(x_2-x_1)\right](x-x_1).\\ \text{Given}\text{points}\text{are}\text{(-3,6) and (6,12)}\text{.}\\ \text{y-6=}\left[(12-6)/(6-(-3))\right](x-(-3)).\\ y-6=(6/9)(x+3).\\ y-6=(2/3)x+2.\\ y=(2/3)x+\mathrm{8.........}(1)\\ f(x)=(2/3)x+8.\\ \text{for}\text{finding}{f}^{-1}(x)\text{replacing}\text{}\text{}\text{the}\text{place}\text{of}x\text{with}y\text{and}\text{place}\text{of}y\text{with}x\text{.}\\ x=(2/3)y+8.\\ (2/3)y=x-8.\\ y=(3/2)x-8\times (3/2).\\ y=(3/2)x-12.\\ f^{-1}(x)=(3/2)x-12.\\ \end{array}$