Chapter 4.7, Problem 34PPS

To determine

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

Answer to Problem 34PPS

Equation for the inverse function $f^{-1}(x)=2x-22.$ .

Explanation of Solution

Given information: Graph of $f(x)$ contains the points (10,16) :graph of $f^{-1}(x)$ contains

the point (3,-16).

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:

If the graph of $f(x)$ contains the point (10, 16), then the graph of $f^{-1}(x)$ ) contains the point (16, 10). For finding the equation for the inverse function $f^{-1}(x)$ ,which contains point (16,10) and (3,-16).

The equation of a function passes through two points is,

  $\begin{array}{l}y-y_1=\left[(y_2-y_1)/(x_2-x_1)\right](x-x_1).\\ \text{Given}\text{points}\text{are}\text{(16,10) and (3,-16)}\text{.}\\ \text{y-10=}\left[(-16-10)/(3-16)\right](x-16).\\ y-10=(-26/-13)(x-16).\\ y-10=2x-32.\\ y=2x-\mathrm{22.........}(1)\\ f^{-1}(x)=(2/3)x+8.\end{array}$