SOLUTION: if 2f(x) - 3f(1/x)= x2 determine f(2)

Algebra ->  Finance -> SOLUTION: if 2f(x) - 3f(1/x)= x2 determine f(2)      Log On


   

Question 892232: if 2f(x) - 3f(1/x)= x2 determine f(2)
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
Given: 2f%28x%29+-+3f%281%2Fx%29+=+x%5E2
let x = 2. Then 2f%282%29+-+3f%281%2F2%29+=+4
Let x = 1/2. Then 2f%281%2F2%29+-+3f%282%29+=+1%2F4
From the second equation, f%281%2F2%29+=+1%2F8+%2B+%283%2F2%29%2Af%282%29.
Substitute this into the first:
2f%282%29+-+3%2F8+-+%289%2F2%29%2Af%282%29+=+4
==> %28-5%2F2%29%2Af%282%29+=+35%2F8 ==>f%282%29+=+-7%2F4