A superadditive function $f(\cdot)$ satisfies the following property $$f\left ( x_{1} +x_{2}\right )\geq f\left ( x_{1} \right ) + f\left ( x_{2} \right )$$

Which of the following functions is a superadditive function for $x > 1$?

1. $e^{x}$
2. $\sqrt{x}$
3. $1/x$
4. $e^{-x}$

edited ago

Solve it using exploring the options

Let $X_{1}$ = 2 and $X_{2}$ = 3

A. f(x) = $e^{x}$

$e^{5}$ > $e^{2}$ + $e^{3}$ ( using the calculator)

it satisfies the condition so option A is correct.

by (380 points)