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 ) = x²

To Find,

The value of f(2).

Solution,

Since we are given that

2f(x)– 3f(1/x) = x²

Putiing x = 2 in this equation,

2f(2)-3f(1/2) = 4

(2f(2)-4)/3 = f(1/2)

Now, putting x = 1/2 we get,

2f(1/2)-3f(2) = 1/4

Now, substituing the value of f(1/2)

2((2f(2)-4)/3)-3f(2) = 1/4

(4f(2)-8)/3 - 3f(2) = 1/4

4f(2) - 8 -9f(2) = 3/4

-5f(2) = 3/4+8

-5f(2) = 35/4

f(2) = -7/4

Hence, the value of f(2) is -7/4.

Answer 2

Given: Here we have given$2f(x)- 3f(1/x ) = x^2$

To find: we have to find the value of f(2)

Solution:

Here we have given $2f(x)- 3f(1/x ) = x^2$

we have to find f(2) so, x=2

$2f(2)- 3f(1/2 ) = 2^2$
$(2f(2)-4)/3 = f(1/2)$....(1)

to find f(1/2) we will put x=1/2

so,

$2f(1/2)- 3f(2 ) = (1/2)^2$

$2f(1/2)-3f(2) = 1/4$

we will put one in above equation

$2((2f(2)-4)/3)-3f(2) = 1/4\\(4f(2)-8)/3 - 3f(2) = 1/4\\4f(2) - 8 -9f(2) = 3/4\\-5f(2) = 3/4+8\\-5f(2) = 35/4\\f(2) = -7/4$

Final answer:

Hence the answer is -7/4