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\(f\left(\frac{1}{3}\right)-2f\left(3\right)=\frac{1}{3}-1=-\frac{2}{3}\Leftrightarrow f\left(\frac{1}{3}\right)=2f\left(3\right)-\frac{2}{3}\)
\(f\left(3\right)-2f\left(\frac{1}{3}\right)=3-1=2\Rightarrow f\left(3\right)-2.\left[2f\left(3\right)-\frac{2}{3}\right]=2\Leftrightarrow-3.f\left(3\right)=2-\frac{4}{3}=\frac{2}{3}\Leftrightarrow f\left(3\right)=-\frac{2}{9}\)
Ta có
+ f(1/2) -f(1/2) = 1/2 -1 =0 ( vô lí)
f(x) không xácđịnh.
ta có
thay x = 2 ta đc
f(2) + 2f(1/2) = 4 (1)
thay x = 1/2 ta đc
f(1/2) + 2f(2) = 1/4
=> 2f(1/2) + 4f(2) = 1/2 (2)
từ (1) và (2) => ta có
2f(1/2) + 4f(2) = 1/2
-
f(2) + 2f(1/2) = 4
=
3f(2) = 1/2 - 4 = -7/2
=> f(2) = -7/6
\(f\left(\frac{1}{3}\right)+2f\left(\frac{1}{\frac{1}{3}}\right)=\left(\frac{1}{3}\right)^2\Rightarrow f\left(\frac{1}{3}\right)+2f\left(3\right)=\frac{1}{9}\)(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) \(\Rightarrow2f\left(3\right)+4f\left(\frac{1}{3}\right)-f\left(\frac{1}{3}\right)-2f\left(3\right)=18-\frac{1}{9}\)
\(\Rightarrow3f\left(\frac{1}{3}\right)=\frac{161}{9}\Rightarrow f\left(\frac{1}{3}\right)=\frac{161}{27}\)
\(f\left(x\right)+3f\left(\frac{1}{x}\right)=x^2\)
Tại x=2 \(\Rightarrow f\left(2\right)+3f\left(\frac{1}{2}\right)=2^2=4\left(1\right)\)
Tại x=\(\frac{1}{2}\)\(\Rightarrow f\left(\frac{1}{2}\right)+3f\left(2\right)=\left(\frac{1}{2}\right)^2=\frac{1}{4}\)
\(\Rightarrow3f\left(\frac{1}{2}\right)+9f\left(2\right)=\frac{3}{4}\)
\(\Rightarrow9f\left(2\right)+3f\left(\frac{1}{2}\right)=\frac{3}{4}\left(2\right)\)
Từ (1)(2) \(\Rightarrow\hept{\begin{cases}f\left(2\right)+3f\left(\frac{1}{2}\right)=4\\9f\left(2\right)+3f\left(\frac{1}{2}\right)=\frac{3}{4}\end{cases}\Rightarrow8f\left(2\right)=\frac{3}{4}-4=\frac{-13}{4}}\)
\(\Rightarrow f\left(2\right)=\frac{-13}{32}\)
\(f\left(3\right)+2f\left(\frac{1}{3}\right)=2.3=6\)=>\(2f\left(\frac{1}{3}\right)=6-f\left(3\right)\Leftrightarrow f\left(\frac{1}{3}\right)=3-\frac{f\left(3\right)}{2}\)
\(f\left(\frac{1}{3}\right)+2f\left(3\right)=2.\frac{1}{3}=\frac{2}{3}\)=> \(3-\frac{f\left(3\right)}{2}+2f\left(3\right)=\frac{2}{3}\Leftrightarrow\frac{3}{2}f\left(3\right)=\frac{2}{3}-3=-\frac{7}{3}\)
\(f\left(3\right)=-\frac{14}{9}\)