Question

Let $f\left(x\right)=\left[x\right]$ and $g\left(x\right)=x-\left[x\right]$ then which one of the following is zero function: ( Where $\left[x\right]$ is the greatest integer function)

• A. $fog$
• B. $f+g$
• C. $f-g$
• D. none of these

Answer 1

The correct option is A $fog$

Given the functions $f\left(x\right)=\left[x\right]$ and $g\left(x\right)=x-\left[x\right]$.

Now,

$g\left(x\right)=\left\{x\right\}$ as $x-\left[x\right]$ represents the fractional part of $x$.

Then $fog=\left[\right\{x\left\}\right]=0$.