Question

1. f(x) = x2 + x and g(x) = 2x + 1
a. Evaluate f(g(3))
b. Evaluate g(f(3))

Answer 1

f(g(3)) = 56

g(f(3)) = 25

Explanation:

fog = f(2x+1)

f(2x+1) = (2x+1)^2 + 2x+1

(2x+1)^2 + 2x+1 = 4x^2+6x+2

f(g(x)) = 4x^2+6x+2

f(g(3)) = 4(3)^2+6(3)+2

f(g(3)) = 56

gof = g(x^2+x)

g(x^2+x) = 2(x^2+x)+1

2(x^2+x)+1 = 2x^2 + 2x + 1

g(f(x)) = 2x^2 + 2x + 1

g(f(3)) = 2(3)^2 + 2(3) + 1

g(f(3)) = 25