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Let 3 f(x)+f ( 1 x )= 1 x +1 What is f(x) equal to?

Options

  1. A1 8 x - x 8 + 1 4
  2. B3 8 x - x 8 + 3 4
  3. C3 8 x + x 8 + 1 4
  4. D3 8 x - x 8 + 1 4

Correct answer

D. 3 8 x - x 8 + 1 4

Step-by-step solution

Given: 3 f(x)+f ( 1 x )= 1 x +1 ....(i) Replacing ( x ) by ( 1 x ) , we get 3 f ( 1 x )+f(x)=x+1 ....(ii) Now, (i) 3-(i i) , we get 8 f(x)= 3 x +3-x-1 f(x)= 3 8 x - x 8 + 1 4 ....(iii)

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