Use the graphs of ƒ and g in the figure to deter...

Question

Use the graphs of ƒ and g in the figure to determine the following function values. y = f(x) ; y=g(x)

a. (ƒ o g ) (2)

Accepted Answer

Welcome back, everyone. In this problem, the graphs of u of x and v of x are shown in the following image. And we want to find the value of u of v of 1. For our answer choices, a is 1, b is 2, c is 3, and d is 4. Now we're trying to find the composition of u of v of 1. And I can rewrite that because u of v of 1, what it really means is that we're putting the function v of 1 into the function u. And when we're evaluating composite functions, we evaluate the innermost one first. So if we can figure out V of 1, then we'll be able to figure out you of V of 1. Now, let's try to figure out V of 1 using our graph. Now, from our graph, V of 1 means that we're trying to find the value of V when x equals 1. So on our graph, when x equals 1, v of 1 v is also 1. It's also 1 on the y axis. Therefore, v of 1 equals 1. So that tells us then that u of v of 1 is the same thing as finding u of 1. Now what's u of 1? Well, we do the same thing again. When x equals 1, what is our graph u or where is our graph u? And x equals 1, then our y value equals 2. So that means you have 1 equals 2. Therefore, u of v of 1 is 2. And when we look back in our answer choices, that would have been answer choice b. Thanks a lot for watching everyone. I hope this video helped.

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Use the graphs of ƒ and g in the figure to determine the following function values. y = f(x) ; y=g(x) <IMAGE>

a. (ƒ o g ) (2)