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Chapter 5: Q 44. (page 269)

The graph of a one-to-one function f is given. 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 inverse of the function in red color is shown below.

Step by step solution

01

Step 1. Given information.

Given a graph of a function falong with y=xas shown below.

02

Step 2. Find the coordinates of f-1 and plot it.

Note that if x,y lies on f, then y,xlies on f-1.

Since the points 2,12,1,0,0,-1,-2,-2 are on the graph f, the points 12,2,0,1,-1,0,-2,-2must be on the graph of .

Keeping in mind that the graph of f-1is the reflection about the

line y=xof the graph of f, draw inverse of the function in red color as shown below.

Blue color denotes the function f.

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Most popular questions from this chapter

The domain of a one-to-one functionf is [0,鈭�), and its range is[5,鈭�). State the domain and the range of f-1.

If f(x)=ax+band g(x)=cx+d, then find: -

(a)f鈭�g

(b)g鈭�f

(c)the domain of f鈭�gand g鈭�f

(d)the conditions for whichf鈭�g=g鈭�f

The function f(x)=|x|is not one-to-one. Find a suitable restriction on the domain of f so that the new function that results is one-to-one. Then find the inverse of f.

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

f(x)=-2xx-1

If g(-5)=3 and g is one-to-one, what is g-1(3)?
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