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BITSAT 2024
Exam
BITSAT
Year
2024
Subject
Mathematics
Chapter
Functions

BITSAT 2024 · Mathematics · Functions

Let [x] denote the greatest integer ≤ x . If f(x)=[x] and g(x)=|x|...

Let [x][x] denote the greatest integer ≤x\leq x. If f(x)=[x]andg(x)=∣x∣f(x)=[x] and g(x)=|x|, then the value of f \left(g \left(\frac{8}{5}\right)\rright)-g\lleft(f \left(-\frac{8}{5}\right)\right)is

Options

  1. A2
  2. B-2
  3. C1
  4. D-1

Correct answer

D. -1

Step-by-step solution

Given, f(x)=[x]andg(x)=∣x∣f(x)=[x] and g(x)=|x| Now, f(−85)=[−85]=−2…(i)g(85)=∣85∣=85…(ii)\begin{gathered} f\left(\frac{-8}{5}\right)=\left[-\frac{8}{5}\right]=-2 \ldots(i)\\ g\left(\frac{8}{5}\right)=\left|\frac{8}{5}\right|=\frac{8}{5}\ldots(ii) \end{gathered} Now, f(g(85))−g(f(−85))=f(85)−g(−2)f\left(g\left(\frac{8}{5}\right)\right)-g\left(f\left(-\frac{8}{5}\right)\right)=f\left(\frac{8}{5}\right)-g(-2) By Eqs. (i) and (ii), =[85]−∣−2∣=1−2=−1\begin{aligned} & =\left[\frac{8}{5}\right]-|-2| \\ & =1-2 \\ & =-1 \end{aligned}
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