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)

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

65.

(f • g)(x) = f(x) • g(x)

(f • g)(x) = (x - 1)(2x^2)

(f • g)(x) = 2x^3 - 2x^2

Domain = All real numbers.

(f/g)(x) = f(x)/g(x)

(f/g)(x) = (x - 1)/(2x^2)

Domain = All real numbers except for x = 0.

You say?

[Eigenvalue]

Yes, C and D are correct.
A. (f+g)(x)=(x-1)+2x²=2x²+x-1
domain: all real numbers, as it is a polynomial
B. (f-g)(x)=x-1-2x²=-2x²+x-1
Domain: all real numbers, as it is a polynomial