Evaluate f(2) given:
f(2/x) + (3/x) + 2x^2 = (x + 3x^3)*f(x/2)
Thanks!
Ok, here's one approach
$\displaystyle f \left( \frac {2}{x} \right) + \frac {3}{x} + 2x^2 = \left( x + 3x^3 \right) f \left( \frac {x}{2} \right)$
When $\displaystyle x = 1$, we have:
$\displaystyle f(2) + 3 + 2 = (1 + 3)f \left( \frac {1}{2} \right)$
$\displaystyle \Rightarrow f(2) = 4 f \left( \frac {1}{2} \right) - 5$ ......(1)
When $\displaystyle x = 4$, we have:
$\displaystyle f \left( \frac {1}{2} \right) + \frac {3}{4} + 32 = (4 + 192)f(2)$
$\displaystyle \Rightarrow f(2) = \frac {f \left( \frac {1}{2} \right) + \frac {131}{4}}{196}$ ...........(2)
Now equate (1) and (2), we get:
$\displaystyle 4 f \left( \frac {1}{2} \right) - 5 = \frac {f \left( \frac {1}{2} \right) + \frac {131}{4}}{196}$
Now we can use that to solve for $\displaystyle f \left( \frac {1}{2} \right)$ and then plug that value into either (1) or (2) to find $\displaystyle f(2)$