Question

For a function f, if f(x + 2) = x² + 4x + 4, then what is the value of f(x)? (the result must be x² but how?)

Options:
A) f(x) = x²
B) f(x) = x² + 4
C) f(x) = x² + 4x
D) f(x) = x² + 2x

Answer 1

To find f(x), we recognize f(x + 2) as a perfect square and reverse the shift by substituting (x + 2) with x, obtaining f(x) = x².

Step-by-step explanation:

The question asks to find the value of f(x) given that f(x + 2) = x² + 4x + 4. We recognize that the right side of the given equation is a perfect square trinomial (x + 2)². To find f(x), we can simply substitute (x + 2) with x in the equation, effectively reversing the function transformation that added 2 to the original argument x. Therefore, f(x) = (x + 2 - 2)² = x², which represents the original function before the shift occurred.