# How many times Continuous

**Calculus**Level 2

Find the number of continuous functions *f* satisfying

\[ x f(y) + yf(x) = (x+y) f(x) \times f(y) \]

where x and y are any real numbers.

Find the number of continuous functions *f* satisfying

\[ x f(y) + yf(x) = (x+y) f(x) \times f(y) \]

where x and y are any real numbers.

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