Question

The function g(x) =x2+3. The function f(x)=g(x+2)

Answer 1

f(x) = g(x + 2)                    Definition

g(x) = x^2 + 3                   Given  

g(x + 2) = (x + 2)^2 + 3     Substitute in g(x) ; make x into x + 2.

f(x) = x^2 + 4x + 4 + 3       expand

f(x) = x^3 + 4x + 7              Collect like terms

The answer is either

f(x) = (x + 2)^2 + 3 or

f(x) = (x^2 + 4x + 7)

Without choices, it's hard to tell which one it is.

Try the second one first.