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

Question

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

Smart Achievers · Accepted Answer

(4)

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

Explanation:

$f (x + 1) = x^{2} - 3 x + 2$

This function is valid for all real values of $x$

Hence, put $x - 1$ in place of $x$ ,

$f (x) = {(x - 1)}^{2} - 3 (x - 1) + 2$

$= x^{2} + 1 - 2 x - 3 x + 3 + 2$

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

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