Let f(x)=\ array ccc -a & if & -a ≤ x ≤ 0 x+a & if & 0 0 and...

Let

f(x)=\left\{

\begin{array}{ccc}-\mathrm{a} & \text{ if } & -\mathrm{a} \leq x \leq 0 \\ x+\mathrm{a} & \text{ if } & 0 < x \leq \mathrm{a}\end{array}

\right.

where

\mathrm{a}>0

and

\mathrm{g}(x)=(f(x \mid)-|f(x)|) / 2

. Then the function

g:[-a, a] \rightarrow[-a, a]

is $Let f(x)=\ array ccc -a & if & -a ≤ x ≤ 0 x+a & if & 0 0 and g(x)=(f(x )-|f(x)|) / 2 . Then the function g:[-a, a]$ $Let f(x)=\ array ccc -a & if & -a ≤ x ≤ 0 x+a & if & 0 0 and g(x)=(f(x )-|f(x)|) / 2 . Then the function g:[-a, a]$ $Let f(x)=\ array ccc -a & if & -a ≤ x ≤ 0 x+a & if & 0 0 and g(x)=(f(x )-|f(x)|) / 2 . Then the function g:[-a, a]$ $Let f(x)=\ array ccc -a & if & -a ≤ x ≤ 0 x+a & if & 0 0 and g(x)=(f(x )-|f(x)|) / 2 . Then the function g:[-a, a]$

Options

Aneither one-one nor onto.
Bonto.
Cboth one-one and onto.
Done-one.

Correct answer

A. neither one-one nor onto.

Step-by-step solution

y=f(x)

$Let f(x)=\ array ccc -a & if & -a ≤ x ≤ 0 x+a & if & 0 0 and g(x)=(f(x )-|f(x)|) / 2 . Then the function g:[-a, a]$

y=f|x|

$Let f(x)=\ array ccc -a & if & -a ≤ x ≤ 0 x+a & if & 0 0 and g(x)=(f(x )-|f(x)|) / 2 . Then the function g:[-a, a]$

y=|f(x)|

$Let f(x)=\ array ccc -a & if & -a ≤ x ≤ 0 x+a & if & 0 0 and g(x)=(f(x )-|f(x)|) / 2 . Then the function g:[-a, a]$

g(x)=\frac{f(|x|)-|f(x)|}{2}

$Let f(x)=\ array ccc -a & if & -a ≤ x ≤ 0 x+a & if & 0 0 and g(x)=(f(x )-|f(x)|) / 2 . Then the function g:[-a, a]$

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