Thread: Problem 41
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Old November 18th, 2007, 07:26 PM
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Quote:
Originally Posted by ThePerfectHacker View Post
1)Let f(x) be a continous function on \mathbb{R} solve the functional equation: f(x+y)=f(x)f(y).
f(x)=c^{x} for some constant c.

then
f(x+y)=c^{x+y}

and
f(x)f(y)=c^{x}c^{y}=c^{x+y}
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