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Chapter 5: Q. 16 (page 256)

Find for the given functionsf,gsuch that

fx=x+1,gx=3x.

(a) f鈭�g4(b)g鈭�f2(c)f鈭�f1(d)g鈭�g0.

Short Answer

Expert verified

The value is

(a) 13(b) 33(c) 32(d) 0.

Step by step solution

01

Part (a) Step 1. Given Information.

The given function are :

fx=x+1,gx=3x.

02

Part (a) Step 2. The evaluation of a functional value.

The functional value are :

(a) f鈭�g4=fg4=f117=117localid="1646900210730" f鈭�g4=fg4=f12=13.

03

Part (b) Step 1. Given Information.

The given function is

fx=x+1,gx=3x.

04

Part (b) Step 2. Evaluation of a functional value.

The value of a function is

g鈭�f2=gf2=g13=33.

05

Part (c) Step 1. Given Information.

The given function is

fx=x+1,gx=3x.

06

Part (c) Evaluation of a functional value.

The value of the function is f鈭�f1=ff1=f2=32.

07

Part (d) Step 1. Given Information.

The given function is

fx=x+1,gx=3x.

08

Part (d) Step 2. Evaluation of a functional value.

The value of the function is

g鈭�g0=gg0=g0=0.

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Most popular questions from this chapter

Findf(3)iff(x)=-4x2+5x.

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

f(x)=2x3x-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?

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).

Solve the equation(15)x=125

and verify your results using a graphing utility.
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