# Wow! My first Function Problem

Calculus Level 4

$\large f\left(\dfrac{x+y}{3}\right)=\dfrac{f(x)+f(y)}{2}$
If a real function $$f$$ satisfies the equation above for all real $$x,y$$, then compute the value of $$\displaystyle\int f(2x^9)\;dx$$

If the answer is of the form $$\dfrac{ c^{M}x^{L}}{N}$$, find $$\lfloor 1000M+29N+8L\rfloor$$

Take $$c$$ as a constant.

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