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 divided by G. Using the graphs below. Alright, so let's recall the domain of F divided by G is going to be equal to the domain of F intersected with the domain of G except where G is equal to zero. Ok, so essentially where F exists and G exists. Okay, We need F and G to exist in order to find F divided by G. Okay, Except where G is zero. Okay, we see if that G is zero, we're dividing by zero. That's going to cause problems. Okay, so let's start by finding the domain of F D F. Well, the domain of F is going to be what function F is in blue here. And we see that for X values from negative five All the way up to positive seven. We have corresponding f values. So the domain of F is going to be negative 5-7 and we're using square brackets to indicate that we include negative five and we include seven because those are solid dots there. Okay. Alright, similarly Fergie the domain of G from the graph. Well, we see that at X equals negative five. We have a value for G that continues all the way along until we get to an X value of six. So the remain of G is going to be negative 5 to 6. Okay, and again, inclusive because we have solid dots here, we have a value at -5 and six. Okay, now the other thing we have to consider is where is G. Zero? Okay well G is equal to zero. G. Is this red curve and it never crosses the X axis, It never touches the X axis. So it's actually never zero. So G equals zero nowhere. Okay so we don't have to worry about that. So now our domain of F divided by G is going to be the intersection of F. But the domain of F. In the domain of G. Okay, so the domain of F divided by G now is equal to the domain of F intersected with the domain of G. K. Because G does not equal zero anywhere. If it did we would have one more value to consider. Okay, so this is going to be negative intersected with negative 56. And when we're intersecting we want to take all of the points that are included in both of these intervals. So what we see is that all of the numbers from negative five up to six are included in both intervals. Okay, Once we get beyond six, that's included in the domain of F. But not in the domain of G. So we don't want to include that in our intersection. Okay and so there we have it. The domain of F divided by G. Just going to be the interval from negative 5 to 6. Including both of those endpoints. And so we have options. That's it for this one. Thanks everyone for watching. See you in the next video.

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

Find the domain of ƒ/g.

Key Concepts

Domain of a Function

Rational Functions

Graph Interpretation

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