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)

b. g (ƒ (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 v of u of 2. For our answer choices, a is 1, b is 2, c is 3, and d is 4. Now, what do we know here? We're dealing with functions on a graph and we want to find the value of v of u of 2. And recall that this is a composite function. And when working with composite functions, we evaluate the innermost function first. So to find v of u of 2, first, we need to find what you have to would be. Now on our graph, notice that our input values x and our output value y is either the function u of x or v of x. So we can use the coordinates on our graphs to figure out what those would be when we input that specific value of x. So from the graph let me put that in red. That's probably closest to our pink graph here. So from the graph, to figure out what u of 2 equals, that means we have to look on our line for u of x when x equals 2. When x equals 2, then we notice that the y value or u would be equal to 3. So that means u of 2 equals 3. What does that tell us? Then this tells us that v of u of 2 then will actually be equal to v of 3. To figure out v of 3, we can go back to our graph. So from the graph k? From the graph, v of 3 means that we want the value of v when x equals 3. And when x equals 3, v function v returns the value 4. So v of 3 equals 4, which then tells us this tells us that v of u of 2 is actually equal to 4. When we go back to our answer choices, that would have been answer choice d. Thanks a lot for watching everyone. I hope this video helped.

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

b. g (ƒ (2))

Key Concepts

Function Composition

Evaluating Functions

Graph Interpretation

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