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 $