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If af(x) + bf(1/x) = x+1, x != 0, find f...

If af(x) + bf(1/x) = x+1, `x != 0`, find f(x).

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To solve the equation \( af(x) + bf\left(\frac{1}{x}\right) = x + 1 \) for \( f(x) \), we can follow these steps: ### Step 1: Substitute \( x \) with \( \frac{1}{x} \) We start by substituting \( x \) with \( \frac{1}{x} \) in the original equation: \[ af\left(\frac{1}{x}\right) + bf(x) = \frac{1}{x} + 1 \] ...
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