# To Check : whether the Graph of f ∘ g is a line.

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

#### Solutions

Chapter 2.6, Problem 68E
To determine

## To Check : whether the Graph of f∘g is a line.

Expert Solution

Yes, the graph is linear with slope = m1m2

### Explanation of Solution

Given information : The functions f(x)=m1x+b1 and g(x)=m2x+b2 are given.

Formula used : The concept of Composition of functions and graphing of functions is used.

Calculation :

f(x)=m1x+b1 And g(x)=m2x+b2

fg=f(g(x))fg=f(m2x+b2)fg=m1(m2x+b2)+b1fg=m1m2x+m1b2+b1

As, the equation is linear,

The line fg of functions f(x)=m1x+b1 and g(x)=m2x+b2 is linear.

Slope = coefficient of x.

Slope = m1m2

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