Question Number 1979 by prakash jain last updated on 27/Oct/15
$${f}:\mathbb{R}\rightarrow\mathbb{R} \\ $$$${g}:\mathbb{R}\rightarrow\mathbb{R} \\ $$$${f}\left({x}+{y}\right)={f}\left({x}\right){g}\left({y}\right)+{g}\left({x}\right){f}\left({y}\right) \\ $$$${g}\left({x}+{y}\right)={f}\left({x}\right){f}\left({y}\right)+{g}\left({x}\right){g}\left({y}\right) \\ $$$${f}\left({x}\right)=? \\ $$$${g}\left({x}\right)=? \\ $$
Answered by Rasheed Soomro last updated on 27/Oct/15
$${f}\left({x}\right)={sinh}\:{x}\:\: \\ $$$${g}\left({x}\right)={cosh}\:{x} \\ $$