Manipulating Radical Functions

Given that $f(x)=\text{-}5\sqrt[4]{x}$ and $g(x)=19\sqrt[4]{x},$ we will find $(f+g)(x)$ and $(f-g)(x).$ Let's begin with the sum of the functions.

Adding Two Functions

Let's recall the definition we will use. $\begin{gathered} (f+g)(x)=f(x)+g(x) \end{gathered}$ From here, we will substitute the given function rules and simplify.

Subtracting Two Functions

Let's recall the rule for subtracting functions. $\begin{gathered} (f-g)(x)=f(x)-g(x) \end{gathered}$ We can proceed in the same way as we did for adding the functions.