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If f(x +y)=f(x).f(y) for all real x, y ...

If `f(x +y)=f(x).f(y)` for all real x, y and `f(0)!=0`, then the function `g(x)=f(x)/(1+{f(x)}^2)` is:

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`f(x+y)=f(x)*f(y)`
`f(x)=e^x`
`g(x)=e^x/(1+e^(2x)`
`g(-x)=(e^(-x))/(1+e^(-2x))=e^x/(1+e^(2x)`
`g(x)=g(-x)`.
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