/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q. 86 If f(x) =log2 x, g(x)=2x, and... [FREE SOLUTION] | 91Ó°ÊÓ

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Chapter 5: Q. 86 (page 309)

If f(x)=log2x,g(x)=2x, and h(x)=4x, find:

(a) role="math" localid="1647339659415" f∘gx. What is the domain of f∘g?

(b) g∘fx. What is the domain of g∘f?

(c) f∘g3

(d) f∘hx. What is the domain of f∘h?

(e) f∘h8

Short Answer

Expert verified

(a)f∘g(x)=x

The domain of f∘g(x)is-∞,∞

(b)role="math" localid="1647340478455" g∘f(x)=x

The domain ofg∘f(x) is-∞,∞

(c)f∘g(3)=3

(d)f∘h(x)=2+log2x

Domain of f∘h(x)is0,∞

(e)f∘h(8)=5

Step by step solution

01

Step 1. Given information 

The Given functions are

f(x)=log2xg(x)=2xh(x)=4x

02

Step 2. Part (a) 

Composition of functionf∘gx

f∘gx=f(g(x))f∘gx=log2g(x)f∘gx=log22xf∘gx=x

So the domain of f∘gxis-∞,∞

03

Step 3. Part (b) 

Composition of functiong∘fx

g∘fx=g(f(x))g∘fx=2f(x)g∘fx=2log2xg∘fx=x

So the domain of g∘fxis-∞,∞

04

Step 4. Part (c) 

Substitute x=3in f∘gx

f∘gx=xf∘g3=3

05

Step 5. Part (d) 

Composition of functionf∘hx

f∘hx=f(h(x))f∘hx=log2h(x)f∘hx=log24xf∘hx=log222+log2xf∘hx=2+log2x

So the domain of f∘hxis0,∞

06

Step 6. Part (e) 

Substitute x=8in f∘hx

f∘hx=2+log2xf∘h8=2+log28f∘h8=2+log223f∘h8=2+3f∘h8=5

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Most popular questions from this chapter

Begin with the graph of y=ex and use transformation to graph the function. Determine the domain, range and horizontal asymptote of the function.

fx=-ex

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).

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localid="1646198784356" d(r)=6.97r-90.39

a. Express the speed rat which the car is traveling as a function of the distance localid="1646198792401" drequired to come to a complete stop

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The graph of an exponential function is given. Match each graph to one of the following functions.

Solve the equation(14)x=164

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