Question

If 2f(x)– 3f(1/x ) = x^2(x≠0), then f(2) is equal to​

Answer 1

Given: 2f(x)– 3f(1/x ) = x^2(x≠0)

To find: f(2)

Solution: From Given condition:-

2f(x)– 3f(1/x ) = x^2 ---equation 1

Replace x equation 1 with 1/x, we got

2f(1/x)– 3f(x ) = (1/x)^2 --equation 2

Now multiply equation 1 with 2 and equation 2 with 3, we get,

4f(x)– 6f(1/x ) = 2(x^2)

6f(1/x)– 9f(x ) = 3((1/x)^2)

Add these equation and we got,

0– 5f(x ) = 2(x^2) + 3((1/x)^2)

Now put x=2 in above equation, we got;

0– 5f(2) = 2(2^2) + 3((1/2)^2)

or,. - 5f(2) = 8 + 3/9

or,. -f(2) = 8/5 + 3/45

or,. f(2) = 75/45

or,. f(2) = -(5/3)

Therefore f(2) = -(5/3)