Let f( {\x})={\\begin{array}{c}- {\a\end{array} , \text{ if }- {\a} \leq {\x} \leq 0 ; {\x}+ {\a} , \text{ if } 0 < {\x} \leq {\a}}. where {\a} > 0 and {\g}( {\x})=(f| {\x}|)-|f( {\x})|) \/ 2. Then the function {\g}:[- {\a}, {\a}] \rightarrow[- {\a}, {\a}] is [8 Apr 2024 Shift 2]

Correct Answer is : neither one-one nor onto.

JEE Main 8 Apr 2024 Shift 2 Solved Paper

Section: Mathematics

Question : 17 of 90

Marks: +1, -0

Let f(x)={

−a	‌ if ‌−a≤x≤0
x+a	‌ if ‌0<x≤a

.
where a>0 and g(x)=(f|x|)−|f(x)|)∕2.
Then the function g:[−a,a]⟶[−a,a] is

[8 Apr 2024 Shift 2]

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