Question

If $f:R\to R$ and $g:R\to R$ are defined by $f\left(x\right)=x-\left[x\right]$ and $g\left(x\right)=\left[x\right]$ for $x\in R$,where $\left[x\right]$ is the greatest integer not exceeding $x$,then for every $x\in R$,$f\left(g\right(x\left)\right)$ is equal to

• A. $x$
• B. $0$
• C. $f\left(x\right)$
• D. $g\left(x\right)$

Answer 1

Answer: (B)

$0$

$f\left(g\right(x\left)\right)=\left[x\right]-\left[x\right]$
As $\left[\right[x\left]\right]=\left[x\right]$
$fog\left(x\right)=\left[x\right]-\left[x\right]=0$