Q. If $f:R \rightarrow R$ and $g:R \rightarrow R$ are defined by $f(x) = x - \lbrack x\rbrack$ and $g(x) = \lbrack x\rbrack$ for $x \in R$, where $\lbrack x\rbrack$ is the greatest integer not exceeding $x$, then for every $x \in R,\ f(g(x))$ is equal to
A) $x$
B) 0
C) $f(x)$
D) $g(x)$
Explanation
(b)
Given, $f(x) = x - \lbrack x\rbrack,\ g(x) = \lbrack x\rbrack$ for $x \in R$.
$\therefore\ \ \ \ \ f\left( g(x) \right) = f(\lbrack x\rbrack)$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \lbrack x\rbrack - \lbrack x\rbrack$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = 0$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.