Thursday, January 21, 2016

functional equations - A non-zero function satisfying g(x+y)=g(x)g(y) must be positive everywhere

Let g:RR be a function which is not identically zero and which satisfies the equation
g(x+y)=g(x)g(y)for all x,yR.



Show that g(x)>0 for all xR.

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