Linear Combination of Functions of Exponential Order

Theorem
Let $f,g \left({t}\right): \R \to \mathbb{F}$ be functions, where $\mathbb{F} \in \left \{{\R,\C}\right\}$.

Let $\lambda, \mu$ be complex numbers.

Suppose $f$ is of exponential order $a$ and $g$ is of exponential order $b$.

Then $\left({\lambda f + \mu g}\right)\left({t}\right) = \lambda f\left({t}\right)+ \mu g\left({t}\right)$ is of exponential order $\max\left({a,b}\right)$.

Proof
Follows from:


 * Scalar Multiple of Function of Exponential Order
 * Sum of Functions of Exponential Order