Let `g(x+(1)/(y)) + g(x-(1)/(y)) = 2g(x) g((1)/(y)) AA x, y in R, y !=0` and `g(0) = 0.` Then find `g(1), g(2)`.

Explanation

To solve the problem, we start with the given functional equation:

\[ g\left(x + \frac{1}{y}\right) + g\left(x - \frac{1}{y}\right) = 2g(x)g\left(\frac{1}{y}\right) \]

for all \( x, y \in \mathbb{R} \) where \( y \neq 0 \), and we know that \( g(0) = 0 \). We need to find \( g(1) \) and \( g(2) \).

### Step 1: Substitute \( x = 1 \) and \( y = 1 \)

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