Q96 / 180 · KCET 2018 · Mathematics

Let $f, g: R \rightarrow R$ be two functions defined as $f(x)=|x|+x$ and $g(x)=|x|-x \forall x \in R$. Then $(f \circ g)(x)$ for $x < 0$ is

  • A
    \( 00 \)
  • B
    \( 4 x \)
  • Correct answer
    C
    \( -4 x \)
  • D
    \( 2 x \)

Solution

$f(x)=|x|+x$ $g(x)=|x|-x$ $f[g(x)]=f[|x|-x]$ $=|| x|-x|+|x|-x[x < 0]$ $=|-2 x|+(-2 x)$ $=-2 x-2 x$ $=-4 x$

Hence, the correct answer is option: 'C'.

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