Two functions g and f are defined in the figure below. g 1...

Two functions g and f are defined in the figure below. g 1 ? 8 5 ? 5 7 ? 0 8 ? 6 Domain of g: {1, 5, 7, 8} Range of g: {0, 5, 6, 8} f 0 ? 3 4 ? 0 5 ? 3 8 ? 1 Domain of f: {0, 4, 5, 8} Range of f: {0, 1, 3} Find the domain and range of the composition f ? g. Write your answers in set notation.

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Transcript

00:01 All right, we have defined the functions g and f.

00:05 We have their domain and their range, and we've been asked to find the domain and the range of the composition f composed with g.

00:16 Now, what we have to remember is that f composed with g means that we're going to take g of x and use it as the input for f.

00:26 So we work this from the inside out.

00:29 So i would have to put in that x value first, and that x value is being plugged into g.

00:36 So i'm going to have to start with values from the domain of g, and we're going to plug it into g, and that's going to turn into the range of g.

00:47 But then i'm going to plug that range of g into the function f, and that output would become the range of f of g.

00:59 So that's what we're looking to see that we can do.

01:02 And i keep in mind that we have to be able to go all the way through this in order for us to be able to claim something is in the domain because every domain has, or every member of the domain, has to have an output.

01:15 So let's just start here.

01:16 Let's start with 1.

01:18 If i plug in a 1 to g, i'm going to be able to get an output of 8.

01:23 And that output of 8 plugged into f will give me an output of 1.

01:29 For my composition.

01:30 So plugging in a 1 gets me an output of 1.

01:36 So there is a value for my domain and my range...

Question

Two functions g and f are defined in the figure below. g 1 ? 8 5 ? 5 7 ? 0 8 ? 6 Domain of g: {1, 5, 7, 8} Range of g: {0, 5, 6, 8} f 0 ? 3 4 ? 0 5 ? 3 8 ? 1 Domain of f: {0, 4, 5, 8} Range of f: {0, 1, 3} Find the domain and range of the composition f ? g. Write your answers in set notation.

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