Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET2014MathematicsFunctions

Let Q be the set of all rational numbers in [0,1] and f:[0,1] [0,1] be defined by f(x)= array r x for x Q 1-x for x Q array . Then, the set S= x [0,21]:(f o f)(x) is equal to

Options

  1. A[0,1]
  2. B-Q
  3. C[0,1]-Q
  4. D(0,1)

Correct answer

A. [0,1]

Step-by-step solution

Given, f(x)= array cc x & for x Q 1-x & for x Q array . is defined for f:[0,1] [0,1] If x is rational, then array rlrl f(x) & =x & f(f(x)) & =f(x)=x array If x is irrational, then aligned f(x) & =1-x f f(x) & =f(1-x)=1-(1-x) & =x aligned f f(x)=x is possible for all values of domain [0,1] .

Practice Functions on Quantrex Academy →

More from Functions

If f : R A , defined by f ( x )= x + 3 x -1 , is an onto function then A = 2025Let g(x)=1+x-[x] and f(x)= cases -1, & x 0 cases ([x] ) denotes the greatest integer less than or equal to (x ). Then for all x , f ( g ( x ))= 2025The domain of the real valued function f(x)= 3 4-x^2 + ₁₀ (x^3-x ) is 2025A real valued function f: A B defined by f(x)= 4-x^2 4+x^2 x A is a bijection. If -4 A then A B= 2025Let [ x ] represent the greatest integer less than or equal to x , x = x -[ x ] , 2 =1.414 and 3 =1.732 . If f(x)= x+ [ x 1+x^2 ] is a real valued function, then f ( 2 )+ f (- 3 )= 2025If the range of the function f(x)=-3 x-3 is 3,-6,-9,-18 , then which one of the following is not in the domain of f ? 2025The domain of the function f(x)= _e ( 1 x^2-4 x+4 ) + ⁻¹ (x^2-2 ) is 2025Consider the following statements Statement-I : A function f : A B is said to be one-one if and only if f(x) f(y) x y Statement-II : A relation f: A B is said to be a function if x 2025 Full Functions list All AP EAMCET PYQs