Prove that, for $f(x), g(x)$ convex, $\alpha_f f(x) + \alpha_g g(x)$ is also convex for $x ∈ S \subset \mathbb R^n$ where $\alpha_f, \alpha_g\ge0$.

Question

I am starting to get some basic knowledge on convex sets and convex functions. I am a bit struck at this question:

If $f(x),g(x)$ are convex, then $\alpha_f f(x) + \alpha_g g(x)$ is also convex for $x \in S \subset \mathbb R^n$ where $\alpha_f, \alpha_g > 0$.