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2022 IIMC keystage3-IWYMIC team Question 2

xIMC · 2022 IIMC keystage3-IWYMIC team

Question 2

The function $f(x)$ is defined for every real number $x$ and satisfies the following condition:
$$f(x)+2f(y)=3f\left(\frac{x+2y}{3}\right)$$
for every two real numbers $x$ and $y$. If $f(2)=1$ and $f(5)=7$, then find $f(2022)$.