Calculate $f (2)$ $f (2)$ , knowing that with any $x \neq 0$ $x ≠ 0$ the correct equality $f (x) + 3 f (\frac{1}{x}) = x^{2}$ $f (x) + 3f (1 / x) = x ^ 2$ ?

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Answer 1 · 2017-09-20T11:28:55

$- \frac{13}{32}$ $-13/32$

Solve the system:

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

for $f (2)$ $f(2)$ .

Or solve

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

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

then evaluate at $x = 2$ $x=2$ .

Calculate f(2)f (2), knowing that with any x≠0x ≠ 0 the correct equality f(x)+3f(1x)=x2f (x) + 3f (1 / x) = x ^ 2 ?