In Exercises 91–94, use the graphs of f and g to evaluate each co...

Question

In Exercises 91–94, use the graphs of f and g to evaluate each composite function.

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Accepted Answer

Hello. Today we are asked to find the value of the composite function G of F. of two. Now this composite function can be rewritten as G. Of F. Of two. So we're going to need to identify the value of F. Of two on the given graph, plugging that value for G. And then identify the value for G. Of that value. So let's go ahead and start by identifying F. Of two. Now the graph for F of X is given to us here and any time that you have the number inside of the parentheses of this function, this is going to be the input value or in other words this is going to be the X value for the graph of F. So in order to figure out what F. Of two is, we're going to identify the point located at the X coordinate two and figure out what the corresponding why value is going to be. So if we take a look at the graph here, let's go ahead and first start at the origin. Now we want to go ahead and go to X is equal to two. So we're going to units to the right and the point located on F of X at X is equal to two is going to be right here. Now we want to go ahead and get the corresponding y value for F. Of two and the corresponding y value is going to be at positive three. So that means that F of two is going to equal to three. And since we know that F of two is equal to three, we're gonna go ahead and plug this in to this composite function. And replacing F of two with three is going to give us G of three. So now we want to go ahead and repeat the process. So again we want to identify the point located X is equal to three on the graph G. Of X. And the answer is going to be the corresponding Y value. So once again we're going to start the origin and since we want to go to X is equal to three, we're going to go three units to the right now. We want to go ahead and identify the point located at X is equal to three on G of X, which is going to be right here. And finally the answer to this problem is going to be the corresponding y value at this coordinate, which is going to be at -3. So G of three is equal to -3, which is going to be the answer to this composite function. And with that being said, the answer to this problem is going to be a So I hope this video helps you in understanding how to approach this problem. And I'll go ahead and see you all in the next video

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In Exercises 91–94, use the graphs of f and g to evaluate each composite function.
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