Question

Let $f(x)=|x-8|$. If $p$ be the sum of all the values of $x$ such that $f(f(f(x)))=2$ and $q$ be the minimum solution of $f ( f ( f ( x )))=2$, then the value of $( p +4 q )$ is

• A. 8
• B. 6
• C. 4
• D. 2

Answer 1

Answer: (A)

Suppose
$ g(x)=f(f(f(x)))-2 $
$g(x)=|||x-8|-8|-8|-2$

$p=48 $
$\gamma=18$
$\beta=14$
$\alpha=2$
$\Rightarrow q =-10 $
$\Rightarrow p +4 q =8$