(1 point) Let f(z) = r² – 6x and g(x) = x-6. Evaluate the following:%3D%3D1. (fo g)(z)=2. (go f)(z)=3. (fo f)(z)=4. (gog)(z)=

Name: (1 point) Let f(z) = r² – 6x and g(x) = x-6. Evaluate the following:%
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Description: (1 point) Let f(z) = r² – 6x and g(x) = x-6. Evaluate the following:%3D%3D1. (fo g)(z)=2. (go f)(z)=3. (fo f)(z)=4. (gog)(z)=

Consider the functions f(x) = x2 - 6x and g(x) = x - 6 If f(x) and g(x) are the two functions then…

Answered: (1 point) Let f(z) = r² – 6x and g(x) =…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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(1 point) Let f(z) = r² – 6x and g(x) = x-6. Evaluate the following:
%3D
%3D
1. (fo g)(z)=
2. (go f)(z)=
3. (fo f)(z)=
4. (gog)(z)=

Expert Solution

Step 1

Consider the functions f(x) = x² - 6x and g(x) = x - 6

If f(x) and g(x) are the two functions then the composite function is denoted as (f o g)(x) and it is defined as,
(f o g) (x) = f(g(x)

Step 2

(1)

(f o g) (x)

By using the definition of composite function,

(f o g) (x) = f(g(x))

Here f(x) = x² - 6x and g(x)= x -6

f(g(x)) = f (x - 6)

Replace x by x - 6 in f(x)

f(g(x)) = (x - 6)² - 6(x - 6)

Expanding this,

f(g(x)) = x² - 12x + 36 - 6x + 36

Therefore, (f o g) (x) = x² - 18x + 72

Step 3

(2)

(g o f) (x)

By using the definition of composite function,

(g o f) (x) = g(f(x))

Here f(x) = x² - 6x and g(x)= x - 6

g(f(x)) = g (x² - 6x)

Replace x by x² - 6x in g(x)

g(f(x)) = (x² - 6x) - 6

Expanding this,

g(f(x)) = x² - 6x - 6

Therefore, (g o f) (x) = x² - 6x - 6

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