Question

Cho hàm số y=F(x) thỏa mãn :
f(x)+2f (1 phần x) = X² +1
tính f(2)

Answer 1

Thay lần lượt \(x=2\) và \(x=\dfrac{1}{2}\) vào ta được:

\(\left\{{}\begin{matrix}f\left(2\right)+2.f\left(\dfrac{1}{2}\right)=2^2+1\\f\left(\dfrac{1}{2}\right)+2.f\left(\dfrac{1}{\dfrac{1}{2}}\right)=\left(\dfrac{1}{2}\right)^2+1\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}f\left(2\right)+2.f\left(\dfrac{1}{2}\right)=5\\f\left(\dfrac{1}{2}\right)+2f\left(2\right)=\dfrac{5}{4}\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}2f\left(\dfrac{1}{2}\right)+f\left(2\right)=5\\2f\left(\dfrac{1}{2}\right)+4f\left(2\right)=\dfrac{5}{2}\end{matrix}\right.\) \(\Rightarrow3f\left(2\right)=\dfrac{5}{2}-5=\dfrac{-5}{2}\)

\(\Rightarrow f\left(2\right)=\dfrac{-5}{6}\)