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

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

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

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

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

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Solution

The correct option is D
$x^{2} - 5 x + 6$

Explanation for the correct option:
Finding the equation:
Given that,
$f (x + 1) = x^{2} - 3 x + 2$
Since, this function is valid for all real values of $x$ .
So, substitute $x - 1$ in place of $x$ , we get
$\begin{array}{rcl} f (x - 1 + 1) & = & {(x - 1)}^{2} - 3 (x - 1) + 2 \\ \Rightarrow & f (x) = x^{2} + 1 - 2 x - 3 x + 3 + 2 \\ = & x^{2} - 5 x + 6 \end{array}$
Hence, the correct option is D.

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