Composite Functions

[nycmath]

Precalculus
Michael Sullivan
Edition 10
Chapter 2, Section 2.1

For the given functions, find A to D. Also, for A to D, find the domain.

A. (f + g)(x)
B. (f - g)(x)
C. (f • g)(x)
D. (f/g)(x)

63.

f(x) = 3x + 4
g(x) = 2x - 3

I will do A and B. I left C and D for others to do.

(f + g)(x) = f(x) + g(x)

(f + g)(x) = 3x + 4 + 2x - 3

(f + g)(x) = 5x + 1

Domain = All real numbers.

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

(f - g)(x) = 3x +4 - (2x - 3)

(f - g)(x) = 3x + 4 - 2x + 3

(f - g)(x) = x + 7

Domain = All real numbers.

You say?