NTA Abhyas JEE Main2020MathematicsFunctionsPractice

If f x = x 2 - x 2 x 2 - x 2 - 2 (where, ⋅ represents the greatest integer part of x ), then the range of f x is

Options

A0 , 1
B- 1 , 1
C0 , ∞
D0 , 1 3

Correct answer

D. 0 , 1 3

Step-by-step solution

We know that, x 2 - x 2 = x 2 ∴ f x = x 2 2 + x 2 = 2 + x 2 - 2 2 + x 2 = 1 - 2 2 + x 2 ∴ 0 ≤ x 2 < 1 ⇒ 2 ≤ x 2 + 2 < 3 2 3 < 2 x 2 + 2 ≤ 1 ⇒ - 2 3 > - 2 2 + x 2 ≥ - 1 ⇒ 1 3 > 1 + - 2 2 + x 2 ≥ 0 Hence, the range of f x is 0 , 1 3

Practice Functions on Quantrex Academy →

More from Functions

Let N denote the set of all positive integers. Consider the sets A = 1, 2, 3, 4, 5 and B = 1, 2, 3, 4, 5, 6, 7 . Let S be the set of all functions f: A B such that f(2) 2 and f(4) 2026 Let f:(1, ) R be a function defined as f(x) = x-1 x+1 . Let f^ i+1 (x) = f(f^i(x)) , i=1, 2, , 25 , where f^1(x)=f(x) . If g(x) + f²⁶(x) = 0 , x (1, ) , then the area of the region 2026 Let f be a polynomial function such that ₂(f(x)) = ( ₂ (2+ 2 3 + 2 9 + ) ) ₃ (1+ f(x) f(1/x) ) , x>0 and f(6)=37 . Then _ n=1 ¹⁰f(n) is equal to ________. 2026 Let f: R R be defined as f(x) = 2x^2 - 3x + 2 3x^2 + x + 3 . Then f is : 2026 Let e be the base of natural logarithm and let f: 1, 2, 3, 4 1, e, e^2, e^3 and g: 1, e, e^2, e^3 1, 1 2 , 1 3 , 1 4 be two bijective functions such that f is strictly decreasing a 2026 Let f: R R be a function such that f(x) + 3f ( 2 - x ) = x , x R . Let the maximum value of f on R be . If the area of the region bounded by the curves g(x) = x^2 and h(x) = x^3 , 2026 The sum of all the integral values of p such that the equation 3 ^2 x + 12 x - 3 = p , x R , has at least one solution, is: 2026 Let A = 1, 2, 3, 4, 5, 6 . The number of one-one functions f: A A such that f(1) 3 , f(3) 4 and f(2) + f(3) = 5 , is __________. 2026 Full Functions list All NTA Abhyas JEE Main PYQs