Question

lf $f$ : $R\to R$ is defined by
$f\left(x\right)=\{\begin{array}{cc}x+4& x<-4\\ 3x+2& -4\le x<4\\ x-4& x\ge 4\end{array}$
then the correct matching of list I to List II is.

List - I	List - II
$A\left)f\right(-5)+f(-4)=$	$i)14$
$B\left)f\right(|f(-8)|)=$	ii $)4$
$C\left)f\right(f(-7)+f\left(3\right))=$	$iii)-11$
$D\left)f\right(f\left(f\right(f\left(0\right)\left)\right)+1=$	$iv)-1$
	v) $1$
	vi) $0$

• A. A-iii , B-vi , C-ii , D- v
• B. A-iii , B-iv , C-ii , D- vi
• C. A-iv , B-iii , C-ii , D- i
• D. A-ii , B-vi , C-v , D- ii

Answer 1

Answer: (A)

A-iii , B-vi , C-ii , D- v

$f(-5)=-5+4=-1;f(-4)=3(-4)+2=-10$
$\therefore f(-5)+f\left(4\right)=-11$
$f\left(|f\right(-8\left)|\right)=f\left(\right(-8+4\left)\right)=f\left(4\right)=4-4=0$
$f\left(f\right(-7\left)\right)tf\left(3\right)=f(-7+4)+3\left(3\right)+2$
$=3(-3)+2+3\left(3\right)+2$
$=4$
$f\left(f\right(f\left(f\right(0\left)\right)\left)\right)+1=f\left(f\right(f\left(2\right)\left)\right)+1=f\left(f\right(8\left)\right)+1$
$=f\left(4\right)+1=0+1=1$