63.8k views
2 votes
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

Consider the following functions f(x) = - sqrt(5 - x) and g(x) = 3 - x Step 1 of 2: Find-example-1
Consider the following functions f(x) = - sqrt(5 - x) and g(x) = 3 - x Step 1 of 2: Find-example-1
Consider the following functions f(x) = - sqrt(5 - x) and g(x) = 3 - x Step 1 of 2: Find-example-2
User Avgn
by
7.8k points

1 Answer

4 votes

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]

User Yasser
by
7.8k points