\(f\left(4\right)+2f\left(\frac{1}{4}\right)=4^2=16\)(1)
\(f\left(\frac{1}{4}\right)+2f\left(\frac{1}{\frac{1}{4}}\right)=\left(\frac{1}{4}\right)^2\)
\(\Rightarrow f\left(\frac{1}{4}\right)+2f\left(4\right)=\frac{1}{16}\Rightarrow2f\left(\frac{1}{4}\right)+4f\left(4\right)=\frac{1}{8}\)(2)
Từ (1) và (2), ta được:
\(2f\left(\frac{1}{4}\right)+4f\left(4\right)-f\left(4\right)-2f\left(\frac{1}{4}\right)=\frac{1}{8}-16\)
\(\Rightarrow3f\left(4\right)=\frac{-127}{8}\Rightarrow f\left(4\right)=\frac{-127}{24}\)