Question

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

• A. 0
• B. 4x
• C. -4x
• D. 2x

Answer 1

Answer: (C)

$f ( x )=| x |+ x =\begin{cases}2 x & \text { if } x \geq 0 \\ 0 & \text { if } x <0\end{cases}$ and $g ( x )=| x |- x =\begin{cases}0 & \text { if } x \geq 0 \\ -2 x & \text { if } x <\,0\end{cases}$
Now for $x <\,0,( f \circ g )( x )= f [ g ( x )]$
$= f [-2 x ]=2(-2 x )=-4 x$