Q. 74 - Precalculus Enhanced with Graphing Utilities

Question

Use the graph of $y=f\left(x\right)$ given in Problem $44$ to evaluate

the following:

(a) $f\left(2\right)$

(b) $f\left(1\right)$

(c) $f^{-1}\left(0\right)$

(d) $f^{-1}(-1)$

Step-by-Step Solution

Answer

According to the graph of$y=f\left(x\right)$ and its inverse

(a)$f\left(2\right)=\frac{1}{2}$

(b)$f\left(1\right)=0$

(c) $f^{-1}\left(0\right)=1$

(d) $f^{-1}(-1)=0$

Step 1. Given data

Graph of $y=f\left(x\right)$ is

Step 2. Graph of the inverse function

Points on the graph of  $y=f\left(x\right)$ are

$(-2,-2),( 0,-1), (1,0),(2,0.5)$

then the points on the inverse function $y=f^{-1}\left(x\right)$will be

$(-2,-2),(-1,0),(0,1),(0.5,2)$

So the graph of the inverse function is 

Step 3. Part (a)

From the graph

$\left(2,\frac{1}{2}\right)$is a point on the graph of $y=f\left(x\right)$

so $f\left(2\right)=\frac{1}{2}$

Step 4. Part (b)

From the graph

$(1,0)$ is a point on the graph of $y=f\left(x\right)$

so$f\left(1\right)=0$

Step 5. Part (c)

From the graph

$(0,1)$is a point on the graph of $y=f^{-1}\left(x\right)$

so$f^{-1}\left(0\right)=1$

Step 6. Part (d)

From the graph

$(-1,0)$is a point on the graph of $y=f^{-1}\left(x\right)$

so$f^{-1}(-1)=0$