Question

Cho hàm số f(x) xác định với mọi x khác 0.

Và f(x) + 3f(\(\frac{1}{x}\)) = x². Tính f (2)

Answer 1

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

\(f\left(\frac{1}{2}\right)+3f\left(2\right)=\frac{1}{4}\)\(\Leftrightarrow\)\(3f\left(\frac{1}{2}\right)+9f\left(2\right)=\frac{3}{4}\) (2) 

(1) - (2) \(\Leftrightarrow\)\(f\left(2\right)+3f\left(\frac{1}{2}\right)-3f\left(\frac{1}{2}\right)-9f\left(2\right)=4-\frac{3}{4}\)

\(\Leftrightarrow\)\(-8f\left(2\right)=\frac{13}{4}\)\(\Leftrightarrow\)\(f\left(2\right)=\frac{-13}{32}\)