Browse Questions

# If $f(x)=\left\{\begin{array}{c,c} |x| &x \leq 1 \\2-x &x>1\end{array}\right.$, then $fof(x)=?$

(A) $fof=\left\{\begin {array}{c,c,c} 2-|x| & if\:x<-1\\ |x| &\:\:if\:\:-1\leq x\leq 1\\|2-x| & if\:x>1\end {array}\right.$ (B) $fof=\left\{\begin {array}{c,c,c} |x| & if\:x<-2\\2- |x| &\:\:if\:\:-2\leq x\leq 2\\|2-x| & if\:x>1\end {array}\right.$ (C) $fof=\left\{\begin {array}{c,c,c} |2-x| & if\:x<-3\\ |x| &\:\:if\:\:-1\leq x\leq 1\\2-|x| & if\:x>1\end {array}\right.$ (D) $fof=\left\{\begin {array}{c,c,c} |x| & if\:x<-1\\2- |x| &\:\:if\:\:-3\leq x\leq 3\\|2-x| & if\:x>3\end {array}\right.$

$fof(x)=\left\{\begin {array}{c,c}f(|x|) & if\:x\leq 1\\f(2-x) & if\:x>1\end {array}\right.$
$=\left\{\begin {array}{c,c,c}||x||=|x| & if\:\:-1\leq x \leq 1\\2-|x| & if\:\:x<-1 \\|2-x| & if\:\:x>1\end {array}\right.$