Question

Consider the following functions f(x) = - sqrt(5 - x) and g(x) = 3 - x Step 1 of 2: Find (g - f)(x) Simplify your answer

Answer 1

We will have the following:

Form the information provided we will have:

`\begin{gathered} (g-f)(x)=(3-x)-(-√(5-x)) \\ \\ \Rightarrow(g-f)(x)=3-x+√(5-x) \end{gathered}`

So, the solution at its simplest is:

`(g-f)(x)=-x+√(5-x)+3`

From the equation we can see that the domain will be restricted by the square root, so the domain will be the following:

`(-\infty,5]`