Question

Given: f(x) = x² and g(x) = 2x + 1, find f[g(x)].

Answer 1

4x² + 4x + 1

Explanation:

To obtain f(g(x)), substitute x = g(x) into f(x)

f(g(x)) = f(2x + 1) = (2x + 1)² = 4x² + 4x + 1

Answer 2

For this case we have by definition that:

`(f_ {0} g) (x) = f [g (x)]`

They tell us that:

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

So:

`(f_ {0} g) (x) = f [2x + 1] = (2x + 1) ^ 2 = (2x) ^ 2 + 2 (2x) (1) + 1 ^ 2 = 4x ^ 2 + 4x + 1`

ANswer:

`f [g (x)] = 4x ^ 2 + 4x + 1`