If f(x)= |x^2-9 x+20 |, then f(x) is equal to : - Vidyadip

MCQ

If $f(x)=\left|x^2-9 x+20\right|,$ then $f(x)$ is equal to :

A
$-2x + 9$ for all $\text{x}\in\text{R}$
B
$2x - 9$ if $4 < x < 5$
✓
$-2x + 9$, if $4 < x < 5$
D
None of these.

✓

Answer

Correct option: C.

$-2x + 9$, if $4 < x < 5$

We have, $f(x)=\left|x^2-9 x+20\right|$
$\text{f}(\text{x})=\begin{Bmatrix} \text{x}^2-9\text{x}+20, & -\infty<\text{x}\leq4 \\ -\big(\text{x}^2-9\text{x}+20\big), & 4<\text{x}<5 \\ \text{x}^2-9\text{x}+20, & 5\leq\text{x}<\infty \end{Bmatrix}$
$\Rightarrow\text{f}\ '(\text{x})=\begin{Bmatrix} 2\text{x}-9\text{x}, & -\infty<\text{x}\leq4 \\ 2\text{x}-9, & 4<\text{x}<5 \\ 2\text{x}-9, & 5\leq\text{x}<\infty \end{Bmatrix}$
$\therefore f\ '(x) = -2x + 9$ for $4 < x < 5$

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