Doubt from functional equation

let f:R\rightarrow R satisfying
f(x+y)=f(x)f(y)f(xy) \thinspace x,y \in \mathcal R
find function
@Hari_Shankar sir , @Jagdish_Singh sir..

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Is it a constant function?

Rechecked it getting e^((x²/2) +x)

I think there would be 3 functions possible one of which will be a constant function like f(x)=1,0,-1

yes prove @akash_2020 ?? its constant function @Samrat_2020

I am getting a constant function @Sneha_2021

yes its correct proof?? @Raunak_2020

Yep sorry only constant function using f'(x)=lit h->0 (f(x+h)-f(x)/h)

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ya thanks i was thinking using substitution techniques getting too long

Actually,I'm not too sure about the constant thing as I'm getting y=(x/x+c) where c is a constant:/

See this @Sneha_2021

cant be constant function by ur mthd @Raunak_2020