Question

[chu thị mai]

cho ham so f(x) xac dinh voi moi x

  Biet vs moi gia tri tuong ung cua x, ta luon co :f(x)+2f(1/x)=x².Tinh f(4)

Answer 1

[Pham Van Hung]

\(f\left(4\right)+2f\left(\frac{1}{4}\right)=4^2=16\)(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: 

           \(2f\left(\frac{1}{4}\right)+4f\left(4\right)-f\left(4\right)-2f\left(\frac{1}{4}\right)=\frac{1}{8}-16\)

\(\Rightarrow3f\left(4\right)=\frac{-127}{8}\Rightarrow f\left(4\right)=\frac{-127}{24}\)