Question

f(x)=1-3x
g(x)=5x^2+3x+2

find f(g) g(f) and f(f) and their domains.

Answer 1

f(g) = 1 - 3g = 1 - 3(5x^2+3x+2) = -15x^2 - 9x - 5
g(f) = 5f^2 + 3f + 2 = 5(1-3x)^2 + 3(1-3x) + 2 = 45x^2 - 39x + 10
f(f) = 1-3f = 1-3(1-3x) = 9x-2

Since f and g are both polynomials, all the domains above are all reals.