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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
Options:
$f(x)=|x|+x$
and
$g(x)=|x|-x \forall x \in R$.
Then $(f \circ g)(x)$ for $x < 0$ is
Solution:
1866 Upvotes
Verified Answer
The correct answer is:
\( -4 x \)
$f(x)=|x|+x$
$g(x)=|x|-x$
$f[g(x)]=f[|x|-x]$
$=|| x|-x|+|x|-x[x < 0]$
$=|-2 x|+(-2 x)$
$=-2 x-2 x$
$=-4 x$
$g(x)=|x|-x$
$f[g(x)]=f[|x|-x]$
$=|| x|-x|+|x|-x[x < 0]$
$=|-2 x|+(-2 x)$
$=-2 x-2 x$
$=-4 x$
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