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

Algebra Level 3

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

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

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

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

Details and assumptions

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


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