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Relations and Functions — MATHS STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 ScienceMATHSRelations and Functions2 Marks
Question
Redefine the function $\text{f(x)}=|\text{x}-2|+|2+\text{x}|, -3\leq\text{x}\leq3.$
✓

Answer

Given that: $\text{f(x)}=|\text{x}-2|+|2+\text{x}|, -3\leq\text{x}\leq3$
since $|\text{x}-2|=-(\text{x}-2),\text{x}<2$
and $|\text{x}-2|=(\text{x}-2),\text{x}\geq2$
$|2+\text{x}|=-(2+\text{x}),\text{x}<-2$
$|2+\text{x}|=(2+\text{x}),\text{x}\geq-2$
Now $\text{f(x)}=|\text{x}-2|+|2+\text{x}|, -3\leq\text{x}\leq3.$
$\begin{cases} -(\text{x}-2)-(2+\text{x}), -3\leq\text{x}<-2\\-(\text{x}-2)-(2+\text{x}), -2\leq\text{x}<2\$\text{x}-2)+(2+\text{x}),2\leq\text{x}\leq3 \end{cases}$
$\therefore\text{f(x)}=\begin{cases}-2\text{x}-3\leq\text{x}-2\\4,-2\leq\text{x}<2\\2\text{x},2\leq\text{x}\leq3\end{cases}$
$\text{f(x)}=\begin{cases}-2\text{x}-3\leq\text{x}-2\\4,-2\leq\text{x}<2\\2\text{x},2\leq\text{x}\leq3\end{cases}$

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