Question

If f(x)=x²-1, and
g(x) = x + 2, then
f(g(x)) = [? ]x² + [ ]x + []

Answer 1

f(g(x)) = x² + 4x + 3

Explanation:

f(x) = x² − 1

g(x) = x + 2

To find the composite f(g(x)), replace x in f(x) with g(x).

f(g(x)) = (g(x))² − 1

Now substitute the expression for g(x).

f(g(x)) = (x + 2)² − 1

Simplify by distributing.

f(g(x)) = x² + 4x + 4 − 1

f(g(x)) = x² + 4x + 3