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

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.