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Let f: R- 0 R be a function such that f(x)-6 f ( 1 x )= 35 3 x - 5 2 . If the _ x 0 ( 1 x +f(x) )= ; , R , then +2 is equal to

Options

  1. A5
  2. B3
  3. C4
  4. D6

Correct answer

C. 4

Step-by-step solution

aligned & f(x)-6 f ( 1 x )= 35 3 x - 5 2 ...(1) & 6 (f ( 1 x )-6 f(x)= 35 x 3 - 5 2 ) & 6 f ( 1 x )-36 f(x)= 210 x 3 - 30 2 ...(2) & (1)+(2) & -35 f(x)= 35 3 [ 1 x +6 x ]- 5 2 (1+6) & -f(x)= 1 3 ( 1 x +6 x )- 1 2 & f(x)=- 1 3 x -2 x+ 1 2 & _ x 0 [ 1 x - 1 3 x -2 x+ 1 2 ]= & =3 & +2 =3+2 1 2 =4 aligned

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