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Q. 73

Expert-verifiedFound in: Page 269

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) $f(-1)$

(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)$f(-1)=0$

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

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

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

The given graph is

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

From the graph

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

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

From the graph

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

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

From the graph

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

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

From the graph

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

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

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