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BITSAT 2020
Exam
BITSAT
Year
2020
Subject
Mathematics
Chapter
Functions

BITSAT 2020 · 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]f(x)=[\mathrm{x}] and g(x)=∣x∣,g(x)=|x|, then the value of f(g(85))−g(f(−85))is\mathrm{f} \left(\mathrm{g} \left(\frac{8}{5}\right)\right)-\mathrm{g}\left(\mathrm{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 that, f(x)=[x] and  g(x)=∣x∣ Now, f(g(85))=g(85)=[85]=1\begin{aligned} &\text{ Given that, } f(x)=[x] \text{\text{ and } } g(x)=|x|\\ &\text{ Now, } \mathrm{f}\left(\mathrm{g}\left(\frac{8}{5}\right)\right)=\mathrm{g}\left(\frac{8}{5}\right)=\left[\frac{8}{5}\right]=1 \end{aligned}and \mathrm{g}\left(\mathrm{f}$\left(-\frac{8}{5}\right)\right)=\mathrm{g}\left(\left[-\frac{8}{5}\right]\right)=\mathrm{g}(-2)=|-2|=2\therefore \mathrm{f}\left(\mathrm{g}\left(\frac{8}{5}\right)\right)-\mathrm{g}\left(\mathrm{f}\left(-\frac{8}{5}\right)\right)=1-2=-1
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