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How to solve inequality with some conditions in Mathematica?

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!
POSTED BY: Peng Liu
2 Replies
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))
POSTED BY: Mariano Gonzalez
Here a solution

Reduce[Exp f > 3 Exp + 1, f]
POSTED BY: Mariano Gonzalez
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