Question

If $f\left(x\right)$ = $|x-1|andg\left(x\right)=f\left[f\left\{f\left(x\right)\right\}\right]$ then for $x>2$, where {.} denotes the gretaest integer function, then g'(x) is equal to

• A. -$1$, if $2\le x<3$
• B. $1$, if $2<x<3$
• C. $1$, for all x > 2
• D. None of these

Answer 1

The correct option is B $1$, if $2<x<3$

$f\left(x\right)=|x-1|$

$\to f\left\{f\right(x\left)\right\}=|\{|x-1|\}-1|$

$\to f\left[f\right\{f\left(x\right)\left\}\right]=|\left[|\right\{|x-1|\}-1|]-1|$

where $\{|x-1|\}\in [0,1)$

For $x\notin Z$

$|\{|x-1|\}-1|\in (0,1)$

$\to f\left[f\right\{f\left(x\right)\left\}\right]=|0-1|=1$