Q. Let $\lbrack x\rbrack$ denote the greatest integer $\leq x$. If $f(x) = \lbrack x\rbrack$ and $g(x) = |x|$, then the value of $f\left( g\left( \frac{8}{5} \right) \right) - g\left( f\left( - \frac{8}{5} \right) \right)$ is
A) 2
B) -2
C) 1
D) -1
Explanation
(d)
Given $f(x) = \lbrack x\rbrack$ and $g(x) = |x|$
Now, $f\left( g\left( \frac{8}{5} \right) \right) = f\left( \frac{8}{5} \right) = \left\lbrack \frac{8}{5} \right\rbrack = 1$
And $g\left( f\left( - \frac{8}{5} \right) \right) = g\left( \left\lbrack - \frac{8}{5} \right\rbrack \right) = g( - 2) = 2$
$\therefore\ \ \ f\left( g\left( \frac{8}{5} \right) \right) - g\left( f\left( - \frac{8}{5} \right) \right) = 1 - 2 = - 1$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.