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Chapter 5: Q9. (page 348)

In Problem 9, state why the graph of the function is one-to-one. Then draw the graph of the inverse function f-1. For convenience (and as a hint), the graph of y=xis also given.

Short Answer

Expert verified

The graph of the inverse function is

Step by step solution

01

Given data

02

Theorem used

The graph of a one-to-one function fand the graph of its inverse f-1are symmetric with respect to the line y=x.

03

According to definition

The order pairs of the given function are3,3,2,0,0,-2and-1,-3

Thus, there are no two distinct inputs that correspond to the same output.

So, the function is one-to-one .

04

To find inverse of the function

The given graph is

Since the points 3,3,2,0,0,2and -1,-3are on the graph of f, the points 3,3,0,2,-2,0and -3,-1must be on the graph of f-1.

The graph of f-1is the reflection about the line y=xof the graph f.

The graph off-1 be

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Most popular questions from this chapter

In Problems 61鈥�72, the function f is one-to-one. Find its inverse and check your answer.

f(x)=3xx+2

Solve the equation22x-1=4

and verify your results using a graphing utility.

In Problems 33-40, the graph of an exponential function is given. Match each graph to one of the following functions.

Evaluate each expression using the values given in the table.

(a) f鈭�g1(b) f鈭�g2(c) g鈭�f2(d) g鈭�f3(e) g鈭�g1(f) f鈭�f3.

In Problems 61鈥�72, the function f is one-to-one. Find its inverse and check your answer.

f(x)=-3x+1x
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