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Question Number 1979 by prakash jain last updated on 27/Oct/15

f:R→R  g:R→R  f(x+y)=f(x)g(y)+g(x)f(y)  g(x+y)=f(x)f(y)+g(x)g(y)  f(x)=?  g(x)=?

$${f}:\mathbb{R}\rightarrow\mathbb{R} \\ $$$${g}:\mathbb{R}\rightarrow\mathbb{R} \\ $$$${f}\left({x}+{y}\right)={f}\left({x}\right){g}\left({y}\right)+{g}\left({x}\right){f}\left({y}\right) \\ $$$${g}\left({x}+{y}\right)={f}\left({x}\right){f}\left({y}\right)+{g}\left({x}\right){g}\left({y}\right) \\ $$$${f}\left({x}\right)=? \\ $$$${g}\left({x}\right)=? \\ $$

Answered by Rasheed Soomro last updated on 27/Oct/15

f(x)=sinh x    g(x)=cosh x

$${f}\left({x}\right)={sinh}\:{x}\:\: \\ $$$${g}\left({x}\right)={cosh}\:{x} \\ $$

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