upper bound of exponential function

Question

I am looking for a tight upper bound of exponential function (or sum of exponential functions):

$e^x<f(x)\;$ when $ \;x<0$ or

$\displaystyle\sum_{i=1}^n e^{x_i} < g(x_1,...,x_n)\;$ when $\;x_i<0$

Thanks a lot!