Use the graphs of f and g to solve Exercises 83–90.

Question

Find the domain of ƒ + g.

Accepted Answer

Hey everyone welcome back in this problem. We are asked to find the domain of F plus G. Using the graph show. Now, let's recall the domain of F. Oops. Plus G. Sorry, is going to be equal to the intersection of the domain of F in the domain of G. Okay, so what we essentially want to do is we want to take all of the points where F exists, all of the points where G exists and find the ones that overlap. Okay, we need F and G to exist in order to find F plus G. Ok, alright, so let's start with the domain of F. The domain of F is going to be while Ephesus blue curve here and we see that it starts when X is negative five. Okay, so from negative five, F goes up exists all the way through here. Okay, up until seven And we're gonna use square brackets because these are filled circles. Okay, so we have a value of negative five. We have a value of -7. So we use square brackets to indicate Kate that we include those points. Similarly for the domain of G. We have a value for G starting at negative five. All the way up until X is positive six. So the domain of G is going to be negative 5 to 6. And again inclusive or including those endpoints because we have values there. So now the domain of F N G is going to be the intersection of the two, so the domain of F plus G is going to be the intersection of negative +57 And -5 6. What this intersection means is find all of the points that are included in both intervals. Hm. And so we see the number or the values from negative five all the way to positive six are included in both intervals. Once we get beyond six, we don't have any numbers included in this domain of G. And so they're not going to be included in our intersection. Okay. And so we get negative 5 to 6 inclusive. And that's gonna be the domain of F plus G. Okay. So we have answer A here. The domain of F plus G is the interval from negative 5 to 6 inclusive. That's it for this one. I hope this video helped see you in the next one.

Use the graphs of f and g to solve Exercises 83–90.

Find the domain of ƒ + g.

Key Concepts

Domain of a Function

Graphical Representation of Functions

Addition of Functions

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