# Calculate f (2), knowing that with any x ≠ 0 the correct equality f (x) + 3f (1 / x) = x ^ 2 ?

Sep 20, 2017

$- \frac{13}{32}$

#### Explanation:

Solve the system:

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

for $f \left(2\right)$.

Or solve

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

for $f \left(x\right) = - \frac{{x}^{4} - 3}{8 {x}^{2}}$

then evaluate at $x = 2$.