Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA2023MathematicsDifferentiationActual

Let a function f be defined on R - 0 and 2 f(x)+f ( 1 x )=x+3 If f is differentiable, then what is (0.5) equal to?

Options

  1. A1 4
  2. B2 3
  3. C2
  4. D4

Correct answer

C. 2

Step-by-step solution

aligned & Since, 2 f ( x )+ f ( 1 x )= x +3 & 2 f ^ ( x )+ f ^ ( 1 x ) (- 1 x ^2 )=1 & Put x =2, 1 2 & 2 f ^ (2)- 1 4 f ^ ( 1 2 )=1...(i) & and, 2 f ^ ( 1 2 )-4 f ^ (2)=1...(ii) aligned after solving (i) & (ii), we get f ^ ( 1 2 )=2, f ^ (2)= 3 4 So, f ^ (0.5)=2

Practice Differentiation on Quantrex Academy →

More from Differentiation

Passage: Let (e^y )^x-y=0 , where y is a function of x whose domain is (0,10] . Question: What is dy dx equal to, given that y=y₀ when x=1 ? 2026If [4] y =x+ x^2+4 , then what is x^2+4 , dy dx equal to ? 2026Passage: Let (e^y )^x-y=0 , where y is a function of x whose domain is (0,10] . Question: What is dy dx equal to ? 2026For the following two (02) items: Consider the function f(x) = cases 4(5^x), & x What is f'(-1) equal to? 2025Consider the following for the two (02) items that follow: Let x = - and y = ^4 - ^4 . What is ( dy dx )^2 equal to? 2025Consider the following for the two (02) items that follow: Let (x+y)^ p+q = x^p y^q , where p , q are positive integers. The derivative of y with respect to x 2025Consider the following for the two (02) items that follow: Let y = ⁻¹ (x - 4x^3 27 ) . What is dy dx equal to? 2025For the following three (03) items: Let y = f(x) = x ⁻¹ x 1 - x^2 + 1 - x^2 . If x = , then what is dy dx equal to? 2025 Full Differentiation list All NDA PYQs