Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA 2016
Exam
NDA
Year
2016
Subject
Mathematics
Chapter
Functions

NDA 2016 · Mathematics · Functions

Let f(x) be the greatest integer function and g(x) be the modulus...

Let f(x)f(x) be the greatest integer function and g(x)g(x) be the modulus function. What is (g∘f)(\mathrm{g} \circ \mathrm{f})\left(-\frac{5}{3}\right)-(\mathrm{f} \circ \mathrm{g})(−53)\left(-\frac{5}{3}\right) equal to?

Options

  1. A–1
  2. B0
  3. C1
  4. D2

Correct answer

C. 1

Step-by-step solution

f(x)→f(x) \rightarrow greatest integer function f(x)=[x]f(x)=[x] g(x)→g(x) \rightarrow modulus function g(x)=∣x∣g(x)=|x| g∘f(x)=g(f(x))fog(x)=f(g(x))=g([x])=f(∣x∣)=∣[x]∣=[∣x∣]gof⁡(−53)=∣[−53]∣;fog(−53)=[∣−53∣]=∣−2∣;=[53]=2;=1gof⁡(−53)−fog(−53)=2−1=1\begin{aligned} & g \circ f(x)=g(f(x)) \quad f o g(x)=f(g(x)) \\ & =g([x]) \quad \quad \quad \quad \quad=f(|x|) \\ & =|[x]| \quad \quad \quad \quad \quad=[|x|] \\ & \operatorname{gof}\left(-\frac{5}{3}\right)=\left|\left[-\frac{5}{3}\right]\right| ; f o g\left(-\frac{5}{3}\right)=\left[\left|-\frac{5}{3}\right|\right] \\ & =|-2| \quad ; \quad=\left[\frac{5}{3}\right] \\ & =2 \quad ; \quad=1 \\ & \operatorname{gof}\left(-\frac{5}{3}\right)-f o g\left(-\frac{5}{3}\right)=2-1=1 \end{aligned}
Practice Functions on Quantrex Academy →

More from Functions

Consider the following statements in respect of the function f(x)=x in the interval… NDA 2026Passage: Consider the curves y=x^2 and y=2|x| . Question: What is the number of points of… NDA 2026If 2f(x)+f(1-x)=x , then what is f(x) equal to ? NDA 2026For the following two (02) items: Consider the function f(x) = 1 - [3] (x-1)^2 . What is… NDA 2025Consider the following for the two (02) items that follow: Let the function y = (1 - x)^… NDA 2025For the following two (02) items: Consider the function f(x) = 10^x - 10^ -x 10^x + 10^… NDA 2025Consider the following for the two (02) items that follow: Let the curve f(x) = |x - 3| .… NDA 2025Consider the following for the two (02) items that follow: Let f = \ (1,1), (2,4), (3,7)… NDA 2025For the following two (02) items: Consider the function f(x) = (x)/(1 - x) (x > 0 , x ≠ 1… NDA 2025Consider the following for the two (02) items that follow: The function f(x) satisfies… NDA 2025Consider the following for the two (02) items that follow: The function f(x) satisfies… NDA 2025Consider the following for the two (02) items that follow: A function f is such that… NDA 2025For the following two (02) items: Consider the function f(x) = (x)/(1 - x) (x > 0 , x ≠ 1… NDA 2025For the following two (02) items: Consider the function f(x) = 10^x - 10^ -x 10^x + 10^… NDA 2025Consider the following for the two (02) items that follow: Let f = \ (1,1), (2,4), (3,7)… NDA 2025Consider the following for the two (02) items that follow: A function f is such that… NDA 2025 Full Functions list Functions JEE Maths PYQsJEE Mathematics PYQs All NDA PYQs