Question
If $f(x)$ is a polynomial function of $x$, satisfying $f(x) \cdot f(y)=f(x)+f(y)+f(x y)-2$ such that $f(1)=2$and $f(2)=5$, then find the value of $f(6)+2009$.
Step 1
Let's substitute $y = \frac{1}{x}$ into this equation. We get: \[f(x) \cdot f\left(\frac{1}{x}\right) = f(x) + f\left(\frac{1}{x}\right) + f(1) - 2\] Show more…
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