If 3 f(x)-2 f ( 1 x )=x , then f^ (2) is equal to

Step-by-step solution

3 f(x)-2 f ( 1 x )=x ...(i) Replace x with 1 x now. From Eq. (i), we get 3 f ( 1 x )-2 f(x)= 1 x ...(ii) aligned & Eq. (i) 2+ Eq. (ii) 3 & 6 f(x)-4 f ( 1 x )=2 x & + -6 f(x)+9 f(1 / x) =2 x+ 3 x & 5 f ( 1 x )=2 x+ 3 x & f ( 1 x )= 2 x 5 + 3 5 x aligned aligned 3 f(x) & =x+2 f ( 1 x ) & =x+2 ( 2 x 5 + 3 5 x ) aligned aligned 3 f(x) & =x+ 4 x 5 + 6 5 x f(x) & = x 3 + 4 x 15 + 2 5 x f^ (x) & = 1 3 + 4 15 - 2 5 x^2 f^ (2) & = 1 3 + 4 15 - 2 5(2)^2 & = 1 3 + 4 15 - 1 10 & = 10+8-3 30 = 15 30 f^ (2) & = 1 2 aligned