If f(x) = x2 + 3x + 1, what is f(x + 2)? Please step by step solving so I many understand.

Question

x2 + 3x + 3

(x + 2)2 + 3(x + 2) + 1

(x + 2)(x2 + 3x + 1)

x2 + 3x + 9

Answer 1

Hi Maria, all you need to do is replace x with x + 2 where ever x occurs in the original function.

Given function:

f(x) = x² + 3x + 1

New function:

f(x + 2) = (x + 2)² + 3(x + 2) + 1

Expand the new function if necessary:

f(x + 2) = x² + 4x + 4 + 3x + 6 + 1

Combine terms:

f(x + 2) = x² + 7x + 11

Questions?

Answer 2

If this is your function below

f(x) = x² + 3x + 1

substitute in (x + 2) for x

f(x + 2) = (x + 2)² + 3(x + 2) + 1

PEMDAS

f(x + 2) = (x² +4x + 4) + 3x + 6 +1

Remove the parentheses

f(x + 2) = x² + 4x + 4 + 3x + 6 +1

Combine like terms

f(x + 2) = x² + 7x + 11

Give it a try, check my math and get back to me.