Find each of the following functions.

Question

f(x) = x2 − 3, g(x) = 5x + 2
(a) f compose g

State the domain of the function. (Enter your answer using interval notation.)

(b) g compose f

State the domain of the function. (Enter your answer using interval notation.)

(c) f compose f

State the domain of the function. (Enter your answer using interval notation.)

(d) g compose g

State the domain of the function. (Enter your answer using interval notation.)

Answer 1

f◦g = f(g) = g^2-3 = (5x+2)^2-3
g◦f = g(f) = 5f+2 = 5(x^2-3)+2
f◦f = f(f) = f^2-3 = (x^2-3)^2-3
g◦g = g(g) = 5g+2 = 5(5x+2)+2

the domain of all polynomials is all real numbers.