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KVPY2014MathematicsFunctions

Let R be the set of all real numbers and let f be a fucntion R to R such that f(x)+ (x+ 1 2 ) f(1-x)=1 , for all x R . Then 2 f(0)+3 f(1) is equal to.

Options

  1. A2
  2. B0
  3. C-2
  4. D-4

Correct answer

C. -2

Step-by-step solution

Given f(x)+ (x+ 1 2 ) f(1-x)=1 ...... (1) but x=0 array l f(0)+ 1 2 f(1)=1 2 f(0)+f(1)=2 ...... (2) array array l put x=1 in (1) f(1)+ 3 2 f(0)=1 2 f(1)+3 f(0)=2 ...... (3) array Solving (2) &(3) we have array l F(0)=2 & f(1)=-2 2 f(0)+f(1)=4-6=-2 array

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