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Chapter 5: Q. 74 (page 269)

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

the following:

(a)f(2)

(b) f(1)

(c) f-1(0)

(d) f-1(-1)

Short Answer

Expert verified

According to the graph ofy=f(x)and its inverse

(a)f(2)=12

(b)f(1)=0

(c)f-1(0)=1

(d)f-1(-1)=0

Step by step solution

01

Step 1. Given data 

Graph of y=f(x)is

02

Step 2. Graph of the inverse function 

Points on the graph of y=f(x)are

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

then the points on the inverse function y=f-1(x)will be

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

So the graph of the inverse function is

03

Step 3. Part (a) 

From the graph

2,12is a point on the graph ofy=f(x)

sorole="math" localid="1646169175430" f(2)=12

04

Step 4. Part (b) 

From the graph

(1,0)is a point on the graph ofy=f(x)

sof(1)=0

05

Step 5. Part (c) 

From the graph

(0,1)is a point on the graph ofy=f-1(x)

sof-1(0)=1

06

Step 6. Part (d) 

From the graph

(-1,0)is a point on the graph ofy=f-1(x)

sof-1(-1)=0

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