Question

Please teach me step by step how to solve:
f(x)=x^2+1 ;Use f(x+2)

Answer 1

if:
f(x)=x^2+1
THEN:
f(x+2) = (x+2)^2+1
You can then expand these brackets (I'm assuming you don't know how to expand these brackets. When anything is to the power of 2, you are multiplying by itself, so we get:
f(x+2) = (x+2)(x+2) +1
When we multiply brackets we use a method called FOIL (First, Outter, Inner, Last).

f(x+2) = (x*x) + (x*2) + (x*2) + (2*2) + 1
f(x+2) = x^2 + 2x + 2x + 4 + 1
f(x+2) = x^2 + 4x + 5

So your answer is:

If:
f(x) = x^2+1
Then:
f(x+2)= x^2+4x+5

Answer 2

1. Pretend you have a variable "u"; u=x+2.
2. You can now re-write f(x+2) as f(u).
3. If f(x) = x^2 + 1, then f(u) = u^2 + 1
4. \[f(u) = u^2 +1 = (x+2)^2 + 1 = (x+2)(x+2) + 1 =\]
\[x^2 + 2x + 2x + 4 + 1 = x^2 + 4x + 4 + 1 = x^2 + 4x + 5\]