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Functions question

2024 · 8 Apr · Shift 2 · Q40
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  5. /2024 · 8 Apr · Shift 2 · Q40

Functions question

2024 · 8 Apr · Shift 2 · Q40

JEE MainMathematicsFunctionsMCQ+4 / −1
Let f(x)={−a if −a≤x≤0x+a if 0<x≤af(x)=\left\{\begin{array}{ccc}-\mathrm{a} & \text { if } & -\mathrm{a} \leq x \leq 0 \\ x+\mathrm{a} & \text { if } & 0\lt x \leq \mathrm{a}\end{array}\right.f(x)={−ax+a​ if  if ​−a≤x≤00<x≤a​ where a>0\mathrm{a}\gt 0a>0 and g(x)=(f(∣x∣)−∣f(x)∣)/2\mathrm{g}(x)=(f(|x|)-|f(x)|) / 2g(x)=(f(∣x∣)−∣f(x)∣)/2. Then the function g:[−a,a]→[−a,a]g:[-a, a] \rightarrow[-a, a]g:[−a,a]→[−a,a] is
  1. A
    neither one-one nor onto.
  2. B
    both one-one and onto.
  3. C
    one-one.
  4. D
    onto
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