54. If f(x) be defined on [-2,2 ] and is given by f(x)={-1 ,-2≤x≤0 and x-1 when 0

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Q. If f(x) be defined on [−2, 2] and is given by

f (x) = \{\begin{cases} - 1, & - 2 \leq x \leq 0 \\ x - 1, & 0 < x \leq 2 \end{cases}

and g(x)

= f (|x|) + |f (x)|

, find g(x).

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 $g (x)$ .

Q. If f : [−2, 2] → R is defined by

f (x) = \{\begin{cases} - 1, & for - 2 \leq x \leq 0 \\ x - 1, & for 0 \leq x \leq 2 \end{cases}

, then
{x ∈ [−2, 2] : x ≤ 0 and f (|x|) = x} =

(a) {−1}
(b) {0}
(c)

\{- \frac{1}{2}\}

(d) ϕ

Q. Let

f (x)

be defined on

[- 2, 2],

and is given by

f (x) = {\begin{matrix} - 1, & - 2 \leq x \leq 0 x - 1, & 0 \leq x \leq 2 \end{matrix},

and

g (x) = f (| x |) + | f (x) |,

then find

g (- 1)

Q. Let

f (x)

be defined on

[- 2, 2]

, and is given by

f (x) = {\begin{matrix} - 1, - 2 \leq x \leq 0 x - 1, 0 \leq x \leq 2 \end{matrix} a n d g (x) = f (| x |) + | f (x) |

, then find

g (x)

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