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Chapter 10: Q. 10.3 (page 992)

For functions f(x)=x2-9and

g(x)=2x+5, find

  1. (f鈭�g)(-2)
  2. (g鈭�f)(-3)
  3. (f鈭�f)(4)

Short Answer

Expert verified

Part a. (f鈭�g)(-2)=-8

Part b. (g鈭�f)(-3)=5

Part c.(f鈭�f)(4)=40

Step by step solution

01

Part (a) Step 1. Find (f∘g)(-2)

Using the definition of composition of functions we have (f鈭�g)(-2)=f(g(-2)).

Find g(-2)where g(x)=2x+5.

(f鈭�g)(-2)=f(2路(-2)+5)(f鈭�g)(-2)=f(-4+5)(f鈭�g)(-2)=f(1)

Find f(1)where f(x)=x2-9

(f鈭�g)(-2)=12-9(f鈭�g)(-2)=1-9(f鈭�g)(-2)=-8

02

Part (b) Step 1. Find (g∘f)(-3)

Using the definition of composition of functions we have (g鈭�f)(-3)=g(f(-3))

Find f(-3)where f(x)=x2-9.

(g鈭�f)(-3)=g((-3)2-9)(g鈭�f)(-3)=g(9-9)(g鈭�f)(-3)=g(0)

Find g(0)where g(x)=2x+5

(g鈭�f)(-3)=2路0+5(g鈭�f)(-3)=0+5(g鈭�f)(-3)=5

03

Part (c) Step 1. Find (f∘f)(4)

Using the definition of composition of functions we have (f鈭�f)(4)=f(f(4)).

Find f(4)where f(x)=x2-9

(f鈭�f)(4)=f(42-9)(f鈭�f)(4)=f(16-9)(f鈭�f)(4)=f(7)

Now find f(7)where f(x)=x2-9.

(f鈭�f)(4)=72-9(f鈭�f)(4)=49-9(f鈭�f)(4)=40

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