Hello. I need help with this problem:
If g and h are real and continuous functions with g(x-y)=g(x)g(y)+h(x)h(y) for all x,y real.
How could I proff they are bounded??
I have think a lot and I found that for example g= cos and h = sin could be these fuctions (but it must to be more).
Also I have tried to replace y=0:
, x=0 :
, x=y :
, x=-y:
.
But I don't get anything.
Thanks for every suggestion.
If g and h are real and continuous functions with g(x-y)=g(x)g(y)+h(x)h(y) for all x,y real.
How could I proff they are bounded??
I have think a lot and I found that for example g= cos and h = sin could be these fuctions (but it must to be more).
Also I have tried to replace y=0:
But I don't get anything.
Thanks for every suggestion.