If f x be defined on -2-2- and is given by f x - left -1- -2 Veq x Veq 0 1 x -1- - 0- x leq 2lend matrix right- and g x - f - x - f x - - Find g x -

We have, { 1, 2 ≤ x ≤ 0 x 1, 0 lt;x ≤ 2 . Now, f(x) = |x| 1, where 2 ≤ x ≤ 2 and f(x) = { 1, 2 ≤ x ≤ 0 (x 1), 0 ≤ x ≤ 1 (x 1), 1 ≤ x ≤ 2 ...

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Standard XII

Mathematics

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If f x be def...

Question

If f(x) be defined on [-2, 2] and is given by $f (x) = {\begin{matrix} - 1, - 2 \leq x \leq 0 x - 1, 0 < x \leq 2 \end{matrix}$
and $g (x) = f (| x |) + | f (x) |$ . Find $g (x)$ .

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Solution

We have,
${\begin{matrix} - 1, - 2 \leq x \leq 0 x - 1, 0 < x \leq 2 \end{matrix}$
Now,
$f (x) = | x | - 1$ , where $- 2 \leq x \leq 2$
and $f (x) = ⎧ ⎪ ⎨ ⎪ ⎩ \begin{matrix} 1, - 2 \leq x \leq 0 - (x - 1), 0 \leq x \leq 1 (x - 1), 1 \leq x \leq 2 \end{matrix}$
$∴ g (x) = f (| x |) + | f (x) | = ⎧ ⎪ ⎨ ⎪ ⎩ \begin{matrix} - x - 2 \leq x \leq 0 00 < x < 1 2 (x - 1), 1 \leq x \leq 2 \end{matrix}$

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If f(x) be defined on [-2, 2] and is given by f(x)={−1, −2≤x≤0x−1, 0<x≤2 and g(x)=f(|x|)+|f(x)|. Find g(x).

We have, {−1, −2≤x≤0x−1, 0<x≤2 Now, f(x)=|x|−1, where −2≤x≤2 and f(x)=⎧⎪⎨⎪⎩1, −2≤x≤0−(x−1), 0≤x≤1(x−1), 1≤x≤2 ∴g(x)=f(|x|)+|f(x)|=⎧⎪⎨⎪⎩−x −2≤x≤00 0<x<12(x−1), 1≤x≤2

If f(x) be defined on [-2, 2] and is given by $f (x) = {\begin{matrix} - 1, - 2 \leq x \leq 0 x - 1, 0 < x \leq 2 \end{matrix}$
and $g (x) = f (| x |) + | f (x) |$ . Find $g (x)$ .