How to solve inequality with some conditions in Mathematica?

Questions
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1

Hello, everyone!
    I want to solve a problem like this. we have known that: (1)e^x*f(x)+f ’ (x)>1, and (2) f(0)=4. How to solve inequality e^xf(x)>3e^x+1.
Thanks!

2

Here a solution

Reduce[Exp f > 3 Exp + 1, f]

3

Reduce[Exp f > 3 Exp + 1, f]

(E^x < 0 && f < E^-x (1 + 3 E^x)) || (E^x > 0 &&
f > E^-x (1 + 3 E^x))