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Functions — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsFunctions3 Marks
Question
If f(x) be defined on [-2, 2] and is given by $\text{f(x)}=\begin{cases}-1,&-2\leq\text{x}\leq0\\\text{x}-1,&0<\text{x}\leq2\end{cases}$ and g(x) = f(|x|) + |f(x)|. Find g(x)
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Answer

We have,
$\text{f(x)}=\begin{cases}-1,&-2\leq\text{x}\leq0\\\text{x}-1,&0<\text{x}\leq2\end{cases}$
Now, $\text{f}\big(|\text{x}|\big)=|\text{x}|-1, $ where $-2\leq\text{x}\leq2$
and $|\text{f(x)}|=​​\begin{cases}1,&-2\leq\text{x}\leq0\\-(\text{x}-1),&0\leq\text{x}\leq1\$\text{x}-1),&1\leq\text{x}\leq2\end{cases}$
$\therefore\ \text{g(x)}=\text{f}(|\text{x}|)+|\text{f}(\text{x})|$
$|\text{f(x)}|=​​\begin{cases}-\text{x},&-2\leq\text{x}\leq0\\0,&0<\text{x}<1\\2(\text{x}-1),&1\leq\text{x}\leq2\end{cases}$

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