Answer:

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

Thay x = 2 vào, ta được:

 \(f\left(2\right)+2f\left(\frac{1}{2}\right)=2^2\Rightarrow f\left(2\right)=2f\left(\frac{1}{2}\right)=4\left(\text{*}\right)\)

Thay \(x=\frac{1}{2}\) vào, ta được: 

\(f\left(\frac{1}{2}\right)+2\left(\frac{1}{\frac{1}{2}}\right)=\left(\frac{1}{2}\right)^2\Rightarrow f\left(\frac{1}{2}\right)+2f\left(2\right)=\frac{1}{4}\Rightarrow2f\left(\frac{1}{2}\right)+4f\left(2\right)=\frac{1}{2}\left(\text{*}\text{*}\right)\)

Từ (*) và (**) \(\Rightarrow f\left(2\right)+2f\left(\frac{1}{2}\right)-\left(2f\left(\frac{1}{2}\right)+4f\left(2\right)\right)=4-\frac{1}{2}\)

\(\Rightarrow f\left(2\right)+2f\left(\frac{1}{2}\right)-2f\left(\frac{1}{2}\right)-4f\left(2\right)=\frac{7}{2}\)

\(\Rightarrow-3f\left(2\right)=\frac{7}{2}\)

\(\Rightarrow f\left(2\right)=\frac{7}{2}.\left(-3\right)=\frac{-7}{6}\)

các bạn giải giúp mk đi ạ !!!!!

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

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

\(\Rightarrow f\left(2\right)=\frac{47}{32}\)

kết quả nhanh nhất 

= 47/32

h mk nha bn hiền 

chúc bn học giỏi

\(f\left(\frac{1}{3}\right)+2f\left(\frac{1}{\frac{1}{3}}\right)=\left(\frac{1}{3}\right)^2\Rightarrow f\left(\frac{1}{3}\right)+2f\left(3\right)=\frac{1}{9}\)(1)

\(f\left(3\right)+2f\left(\frac{1}{3}\right)=3^2\Rightarrow2f\left(3\right)+4f\left(\frac{1}{3}\right)=18\)(2)

Từ (1) và (2) \(\Rightarrow2f\left(3\right)+4f\left(\frac{1}{3}\right)-f\left(\frac{1}{3}\right)-2f\left(3\right)=18-\frac{1}{9}\)

\(\Rightarrow3f\left(\frac{1}{3}\right)=\frac{161}{9}\Rightarrow f\left(\frac{1}{3}\right)=\frac{161}{27}\)

Cho \(x=\frac{1}{4}\) \(\Rightarrow f\left(\frac{1}{4}\right)+3f\left(\frac{1}{4}\right)=\left(\frac{1}{4}\right)^2\)\(\Rightarrow4f\left(\frac{1}{4}\right)=\frac{1}{16}\Rightarrow f\left(\frac{1}{4}\right)=\frac{1}{64}\)

Cho \(x=2017\Rightarrow f\left(2017\right)+3f\left(\frac{1}{4}\right)=2017^2\)\(\Rightarrow f\left(2017\right)=2017^2-3.\frac{1}{64}=2017^2-\frac{3}{64}\)

\(=4068288,953\approx4068289\)

Xét hàm số f(x) thỏa mãn \(f\left(x\right)+3f\left(\frac{1}{x}\right)=x^2\). Với mọi \(x\inℤ\)

Đúng với x = 2

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

=> \(3f\left(2\right)+f\left(\frac{1}{2}\right)=\frac{1}{4}\Rightarrow9f\left(2\right)+3f\left(\frac{1}{2}\right)=\frac{3}{4}\)(2)

Lấy (2) - (1) ta có:

\(8f\left(2\right)=\frac{3}{4}-4=\frac{-13}{4}\)

\(\Rightarrow f\left(2\right)=\frac{-13}{4}\)

*P/s: Mk ko chắc*