Solving Functional Equations (for beginners)

In this video, we explore a fascinating functional equation problem. Given that \[ f(x) + 2f\left(-\frac{1}{x}\right) = x + \frac{12}{x^2}, \]
we aim to find the value of \( f(2) \). Follow along as we demonstrate step-by-step reasoning, leveraging substitution and algebraic manipulation to derive the solution. This methodical approach highlights techniques useful for solving similar functional equations in math Olympiads and high school competitions.

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