Let $f(x)=[x]$ and $g(x)=|x|.$ Then gof $(\frac{-5}{3})-fog(\frac{-5}{3})$ where [x] is greatest integer valued function and [x] is modulus function.
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 1
$gof (\frac{-5}{3})-fog(\frac{-5}{3})$
so $g([\frac{-5}{3}])-f(|\frac{-5}{3}|)$
$=g(-2)-f(\frac{5}{3})$
$=|-2|-[\frac{5}{3}]=2-1=1$