Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA 2018
Exam
NDA
Year
2018
Subject
Mathematics
Chapter
Functions

NDA 2018 · Mathematics · Functions

If f(x)= x-1 x-4 defines a function of R , then what is its domain?

If f(x)=x−1x−4f(x)=\frac{\sqrt{x-1}}{x-4} defines a function of RR, then what is its domain?

Options

  1. A(−∞,4)∪(4,∞)(-\infty, 4) \cup(4, \infty)
  2. B[4,∞][4, \infty]
  3. C(1,4)∪(4,∞)(1,4) \cup(4, \infty)
  4. D[1,4)∪(4,∞)[1,4) \cup(4, \infty)

Correct answer

D. [1,4)∪(4,∞)[1,4) \cup(4, \infty)

Step-by-step solution

f(x)=x−1x−4f(x) is defined for (x−1)≥0⇒x≥1 and x−4≠0⇒x≠4∴ Domain of f(x)=1≤x<∞−{4} or, x=[1,4)∪(4,∞).\begin{array}{ll}& f(x)=\frac{\sqrt{x-1}}{x-4} \\ & f(x) \text{ is defined for }(x-1) \geq 0 \Rightarrow x \geq 1 \text{ and } x-4 \neq 0 \\ \Rightarrow & x \neq 4 \\ \therefore & \text{ Domain of } f(x)=1 \leq x < \infty-\{4\} \\ \text{ or, } & x=[1,4) \cup(4, \infty).\end{array}
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