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If e^x + e^(f(x)) = e then domain of f(x...

If `e^x + e^(f(x)) = e` then domain of f(x) is

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`e^x+e^y=e`
`e^y=e-e^x`
taking log both side
`loge^y=ln(e-e^x)`
`yloge=log(e-e^x)`
`y=f(x)=log(e-e^x)`
`e-e^x>0`
`e>e^x`
...
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