1. ## Hard Function

Evaluate f(2) given:

f(2/x) + (3/x) + 2x^2 = (x + 3x^3)*f(x/2)

Thanks!

2. Originally Posted by Ideasman
Evaluate f(2) given:

f(2/x) + (3/x) + 2x^2 = (x + 3x^3)*f(x/2)

Thanks!
Ok, here's one approach

$f \left( \frac {2}{x} \right) + \frac {3}{x} + 2x^2 = \left( x + 3x^3 \right) f \left( \frac {x}{2} \right)$

When $x = 1$, we have:

$f(2) + 3 + 2 = (1 + 3)f \left( \frac {1}{2} \right)$

$\Rightarrow f(2) = 4 f \left( \frac {1}{2} \right) - 5$ ......(1)

When $x = 4$, we have:

$f \left( \frac {1}{2} \right) + \frac {3}{4} + 32 = (4 + 192)f(2)$

$\Rightarrow f(2) = \frac {f \left( \frac {1}{2} \right) + \frac {131}{4}}{196}$ ...........(2)

Now equate (1) and (2), we get:

$4 f \left( \frac {1}{2} \right) - 5 = \frac {f \left( \frac {1}{2} \right) + \frac {131}{4}}{196}$

Now we can use that to solve for $f \left( \frac {1}{2} \right)$ and then plug that value into either (1) or (2) to find $f(2)$

3. Thanks. Jhevon, would you mind checking to see if you got this answer:

f(2) = 136/783

What I did was solve for f(1/2) as you instructed to get 4051/3132 then plugged this into equation (1) to solve for f(2).

Many thanks.

4. Originally Posted by Ideasman
Thanks. Jhevon, would you mind checking to see if you got this answer:

f(2) = 136/783

What I did was solve for f(1/2) as you instructed to get 4051/3132 then plugged this into equation (1) to solve for f(2).

Many thanks.
That's what i got. that's the answer provided my equations for (1) and (2) were correct. you might want to double check my computations for both to be safe