Combination Theorem for Continuous Functions/Real

Theorem
Let $X$ be one of the standard number fields $\Q, \R, \C$.

Let $f$ and $g$ be functions which are continuous on an open subset $S \subseteq X$.

Let $\lambda, \mu \in X$ be arbitrary numbers in $X$.

Then the following results hold:

Also see

 * Combination Theorem for Limits of Functions