Question

If $f(x + 1) = x^2 - 3x + 2$, then f (x) is equal to:

• A. $x^2 - 5x - 6$
• B. $x^2 + 5x - 6$
• C. $x^2 + 5x + 6$
• D. $x^2 - 5x + 6$

Answer 1

Answer: (D)

$x^2 - 5x + 6$

Answer 2

Given function is : $f (x + 1) = x^2 - 3x + 2$ This function is valid for all real values of x. So, putting x - 1 in place of x, we get $f (x) = f (x - 1 + 1)$ $\Rightarrow \, f (x) = (x - 1)^2 - 3(x - 1) + 2$ $\Rightarrow \, f (x) = x^2 - 2x + 1 - 3x + 3 + 2$ $f (x) = x^2 - 5x + 6$