An interesting function

Calculus Level 4

$$f(x)$$ is a non-negative function defined for $$x\geq1$$ such that the inequality $$f '(x)\leq m \cdot f(x)$$ holds everywhere in the domain for some positive real number $$m$$. If $$f(1)=0$$ then find the value of $$f(e)+f(e^2)$$.

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