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If f (x) = $| x^{2} - 5 x + 6 |$ then $f^{1} (x)$ equals.

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$2 x - 5 if 2 < x < 3$

$5 - 2x if x \leq 3$

$5 - 2 x if 2 < x < 3$

$2 x - 5 if x > 2$

answer is B.

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Detailed Solution

$\begin{array}{l} f (x) = | x^{2} - 5 x + 6 | \\ f (x) = {\begin{cases} x^{2} - 5 x + 6 i f x < 2, x > 3 \\ - x^{2} + 5 x - 6 i f 2 < x < 3 \end{cases} \\ f^{|} (x) = 5 - 2 x f o r 2 < x < 3 \end{array}$

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