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Chapter 5: Q 47. (page 269)

In Problem, 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 = x is also given.

Short Answer

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Step by step solution

01

Step 1. Given information

02

Step 2. Graph of f-1

We know that the graph of a function f and the graph of its inverse is symmetric with respect to the line y = x.

For every point (x, y) on the graph of f(x), there will be a symmetric point (y, x) which will be on the graph of f-1(x).

From the given graph of f(x), the only point present is (0,1).

So, the corresponding point on the graph of f-1(x)is (1,0).

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Most popular questions from this chapter

Ideal Body Weight One model for the ideal body weight W for men (in kilograms) as a function of height h (in inches) is given by the function

W(h)=50+2.3h-60

(a) What is the ideal weight of a 6-foot male?

(b) Express the height has a function of weight W.

(c) Verify that h=Whis the inverse of W=Whby showing that role="math" localid="1646158219737" h(W(h))=h and W(h(W))=W.

(d) What is the height of a male who is at his ideal weight of 80 kilograms?

[Note: The ideal body weight W for women (in kilograms) as a function of height h (in inches) is given byrole="math" localid="1646159253780" Wh=45.5+2.3(h-60).

The domain of a one-to-one functiong is(-鈭�,0) , and its range is[0,鈭�). State the domain and the range ofg-1 .

A function fhas an inverse function. If the graph of f lies in quadrant I in which quadrant does the graph of f-1 lie?

solve each equation. Verify your results using a graphing utility.

3x2-7=272x

True or Falsefgx=fx.gx.
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