Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
BITSAT 2014
Exam
BITSAT
Year
2014
Subject
Mathematics
Chapter
Functions

BITSAT 2014 · Mathematics · Functions

The domain of the function f(x)= _ 2 (- _ 1/2 (1+ 1 x^ 1 / 4 )-1) is

The domain of the function f(x)=log⁡2f(x)=\log _{2}\left(-\log _{1/2}\left(1+\frac{1}{x^{1 / 4}}\right)-1\right) is

Options

  1. A(0,1)
  2. B(0,1]
  3. C[1,∞)[1, \infty)
  4. D(1,∞)(1, \infty)

Correct answer

A. (0,1)

Step-by-step solution

f(x)f(x) is defined if −log⁡1/2(1+1x1/4)−1>0⇒log⁡1/2(1+1x1/4)<−1⇒1+1x1/4>(12)−1⇒1x1/4>1⇒0<x<1\begin{array}{l} -\log _{1/2}\left(1+\frac{1}{x^{1 / 4}}\right)-1 > 0 \\ \Rightarrow \quad \log _{1/2}\left(1+\frac{1}{x^{1 / 4}}\right) < -1 \\ \Rightarrow \quad 1+\frac{1}{x^{1 / 4}} > \left(\frac{1}{2}\right)^{-1} \\ \Rightarrow \quad \frac{1}{x^{1 / 4}} > 1 \\ \Rightarrow \quad 0 < x < 1 \end{array}
Practice Functions on Quantrex Academy →

More from Functions

Let [x] denote the greatest integer ≤ x . If f(x)=[x] and g(x)=|x| , then the value of f… BITSAT 2024Number of real solution of 5- _2|x| =3- _2|x| is equal to BITSAT 2024f(x)=( x)/([(2 x)/(π)]+(1)/(2)) , where x is not an integral multiple of π and [.]… BITSAT 2024The function f: R arrow R defined by f(x)= x 1+x^2 is BITSAT 2024If f: R arrow R, g: R arrow R are defined by f(x)=5 x-3, g(x)=x^2+3 , then g o f^ -1 (3)… BITSAT 2024The domain of the real valued function f(x)= (2 x^2-7 x+5)/(3 x^2-5 x-2) is BITSAT 2024If a function f: R-\ l\ arrow R-\ m\ defined by f(x)=(x+3)/(x-2) is a bijection, then 3… BITSAT 2024f(x)= x+ x, g(x)=x^2-1 , then g(f(x)) is invertible if BITSAT 2024Let the function g:(-∞, ∞) arrow (-(π)/(2), (π)/(2)) be given by g(u)=2 ^ -1… BITSAT 2024The domain of the function f(x)= x- 1-x^2 is BITSAT 2023Consider the function f in A=R-\ (2)/(3)\ defined as f(x)=(4 x+3)/(6 x-4) , then f^ -1 is… BITSAT 2023If f(x)= x 1+x^2 , then (fof of) (x) is BITSAT 2023If g(x)=x^2+x-2 and (1)/(2) g o f(x)=2 x^2-5 x+2 then f(x) is equal to BITSAT 2022The domain of the function f(x)= 1 x^ 12 -x^ 9 +x^ 4 -x+1 is given by BITSAT 2021Let [x] denote the greatest integer ≤ x . If f(x)=[x] and g(x)=|x|, then the value of f… BITSAT 2020The domain of the function f(x)= x- 1-x^ 2 is BITSAT 2020 Full Functions list Functions JEE Maths PYQsJEE Mathematics PYQs All BITSAT PYQs