   Chapter 1.3, Problem 61E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# Let f and g be linear functions with equations f(x) = m1x + b1, and g(x) = m2x + b2. Is f ◦ g also a linear function? If so, what is the slope of its graph?

To determine

To check: Whether fg is linear if f and g are linear; find the slope of the graph fg if it is linear.

Explanation

Given:

The linear functions are f(x)=m1x+b1,g(x)=m2x+b2 .

Calculation:

The composite function (fg)(x) is defined as follows.

(fg)(x)=f(g(x))

Substitute m2x+b2 for x in f(x) and find the composition function (fg)(x)

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