f(xy) = f(x) * f(y)

Algebra Level 3

\(f: \mathbb{R} \rightarrow \mathbb{R}\) is a function that satisfies the following 2 conditions:

1) \( f(xy) = f(x)\cdot f(y) \) for all values of \(x, y\)

2) \( f(0) \neq 0 \).

What is the value of \( f(2) \)?

Details and assumptions

Read Functions - Definitions and Terminology if you do not know what \(f: \mathbb{R} \rightarrow \mathbb{R}\) means.

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