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Q. 73

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Found in: Page 269

### Precalculus Enhanced with Graphing Utilities

Book edition 6th
Author(s) Sullivan
Pages 1200 pages
ISBN 9780321795465

# Use the graph of $y=f\left(x\right)$ given in the Problem $43$ to evaluate the following:(a) $f\left(-1\right)$(b) $f\left(1\right)$ (c) ${f}^{-1}\left(1\right)$ (d) ${f}^{-1}\left(2\right)$

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

(a)$f\left(-1\right)=0$

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

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

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

See the step by step solution

## 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

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

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

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

So the graph of the inverse function is

## Step 3. Part (a)

From the graph

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

sorole="math" localid="1646167799685" $f\left(-1\right)=0$

## Step 4. Part (b)

From the graph

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

sorole="math" localid="1646167820149" $f\left(1\right)=2$

## Step 5. Part (c)

From the graph

$\left(1,0\right)$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

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

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