Question

f for non zero x : 2 f(x) + 3 f(1/x) = x find find f(2) class 11

Answer 1

Answer :

f(2) = -1/2

Solution :

• Given : 2f(x) + 3f(1/x) = x
• To find : f(2) = ?

We have ;

2f(x) + 3f(1/x) = x ---------(1)

Now ,

Replacing x by 1/x in eq-(1) , we get ;

=> 2f(1/x) + 3f( 1/(1/x) ) = 1/x

=> 2f(1/x) + 3f(x) = 1/x

=> 3f(x) + 2f(1/x) = 1/x -------(2)

Now ,

Multiple eq-(1) by 2 , we get ;

=> 2•[ 2f(x) + 3f(1/x) ] = 2•x

=> 4f(x) + 6f(1/x) = 2x ---------(3)

Also ,

Multiplying eq-(2) by 3 , we get ;

=> 3•[ 3f(x) + 2f(1/x) ] = 3•(1/x)

=> 9f(x) + 6f(1/x) = 3/x --------(4)

Now ,

Subtracting eq-(3) from (4) , we get ;

=> [9f(x) + 6f(1/x)] - [4f(x) + 6f(1/x)] = 3/x - 2x

=> 9f(x) + 6f(1/x) - 4f(x) - 6f(1/x) = 3/x - 2x

=> 5f(x) = 3/x - 2x

=> 5f(x) = (3 - 2x²)/x

=> f(x) = (3 - 2x²)/5x ---------(5)

Now ,

Putting x = 2 in eq-(5) , we get ;

=> f(x) = (3 - 2x²)/5x

=> f(2) = (3 - 2•2²)/(5•2)

=> f(2) = (3 - 8)/(5•2)

=> f(2) = -5/(5•2)

=> f(2) = -1/2

Hence , f(2) = -1/2