If f(x + 1) = x2 - 3x + 2, then f (x) is equal to:

Question

If f(x + 1) = x2 - 3x + 2, then f (x) is equal to: (A) x2 - 5x - 6 (B) x2 + 5x - 6 (C) x2 + 5x + 6 (D) x2 - 5x + 6

Tardigrade Admin · Accepted Answer

Given function is: f (x + 1) = x2 - 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) ⇒ f (x) = (x - 1)2 - 3(x - 1) + 2 ⇒ f (x) = x2 - 2x + 1 - 3x + 3 + 2 f (x) = x2 - 5x + 6

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

$x^{2} - 5 x - 6$

$x^{2} + 5 x - 6$

$x^{2} + 5 x + 6$

$x^{2} - 5 x + 6$

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

Q. If f(x+1)=x2−3x+2, then f (x) is equal to:

x2−5x−6

x2+5x−6

x2+5x+6

x2−5x+6