Question

If $f\left(x\right)=\left[x\right]$ and $g\left(x\right)=x-\left[x\right]$, then which of the following is the zero function?

• A. $(f+g)(x)$
• B. $(fg)(x)$
• C. $(f-g)(x)$
• D. None of these

Answer 1

Answer: (D)

$\left(f+g\right)\left(x\right)=f\left(x\right)+g\left(x\right)=\left[x\right]+\left(x-\left[x\right]\right)=x$
$\left(fg\right)\left(x\right)=f\left(x\right).g\left(x\right)=\left[x\right]\left(x-\left[x\right]\right)$
$\left(f-g\right)\left(x\right)=f\left(x\right)-g\left(x\right)=\left[x\right]-\left(x-\left[x\right]\right)=2\left[x\right]-x$