Question

Let $[x]$ denote the greatest integer less than or equal to $x$ . If $f(x)=[x]$ 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. 0
• E. $-1$

Answer 1

Answer: (E)

Given that, $f(x)=[x]$ and $g(x)=|x|$ Now, $f\left(g\left(\frac{8}{5}\right)\right)=f\left(\frac{8}{5}\right)=\left[\frac{8}{5}\right]=1$ and $g\left(f\left(-\frac{8}{5}\right)\right)=g\left(\left[-\frac{8}{5}\right]\right)$
$=g(-2)=|-2|=2$
$\therefore$ $f\left(g\left(\frac{8}{5}\right)\right)-g\left(\left[-\frac{8}{5}\right]\right)=1-2=-1$