Q. 73 - Precalculus Enhanced with Graphing Utilities

Question

Use the graph of $y=f\left(x\right)$ given in the Problem $43$ to evaluate the following:

(a) $f(-1)$

(b) $f\left(1\right)$ 

(c) $f^{-1}\left(1\right)$ 

(d) $f^{-1}\left(2\right)$

Step-by-Step Solution

Answer

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

(a)$f(-1)=0$

(b)$f\left(1\right)=2$

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

(d)$f^{-1}\left(2\right)=1$

Step 1. Given data

The given graph is

Step 2. Graph of the inverse function

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

$(-2,-2),(-1,0),(0,1),\&(1,2)$

then the points of the function $f^{-1}\left(x\right)$ will be

$(-2,-2),(0,-1),(1,0),\&(2,1)$

So the graph of the inverse function is

Step 3. Part (a)

From the graph

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

so $f(-1)=0$

Step 4. Part (b)

From the graph

$(1,2)$is a point on the graph of $f\left(x\right)$

so $f\left(1\right)=2$

Step 5. Part (c)

From the graph

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

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

Step 6. Part (d)

From the graph

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

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