If 4 f(x)-f ( 1 x )= (2 x+ 1 x ) (2 x- 1 x ) , then what is f(2) equal to?

Step-by-step solution

4 f(x)-f ( 1 x )= (2 x+ 1 x ) (2 x- 1 x )4 f ( x )- f ( 1 x )=4 x ^2- 1 x ^2 ...(i) Replace x by 1 x we get 4 f ( 1 x )-f(x)= 4 x^2 -x ...(ii) from 4 ( i) + (ii) 16 f(x)-4 f ( 1 x )=16 x^2- 4 x^2 aligned & 16 f(x)-4 f ( 1 x )=16 x^2- 4 x^2 & 4 f ( 1 x )-f(x)= 4 x^2 -x aligned aligned & 15 f ( x )=15 x ^2 & f ( x )= x ^2 aligned Now, f(2)=2^2=4 .