The graphs of two functions ƒ and g are shown in the figures.
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Question

The graphs of two functions ƒ and g are shown in the figures.

Graph of function f with points (1,-2) and (4,10) marked on a grid.

Find (g∘ƒ)(3).

Accepted Answer

Hey, everyone in this problem, we're asked to find the value of the expression using the graph given below the expression we're asked to evaluate is the composition of functions G of F evaluated at four. And we're given two graphs, we're given the graph of F of X. On the left hand side, it says a linear function looks like a straight line. And we're given two points on that graph, we have the 0.1 negative two and we have the 0.4 10. Now the function G of X is shown on the right, it says a quadratic looking function parabola that opens upwards. And again, we're given two points on this curve. We're given two negative 10 and we're given the 100. 70. Now we have four answer choices. We have a 10 B 70 C four and D negative two. So let's start by writing out what we were given. So we were given the composite function G of F evaluated at and we aren't given any information about this composite function G of F. So how can we evaluate it at a point? Let's break it down. We're given information about F on its own and G on its own. So let's try to rewrite this composite function recall. We can write G of F evaluated at four as G of F at four. Hm. So we have the function G evaluated at the function F evaluated at four. All right. So how do we evaluate this? Well, we can't evaluate this outside function G yet because we don't know what we're evaluating it at, we're evaluating it at some function value which we don't know yet. So what we need to do is work from the inside. So let's first evaluate F at four. Now we can look at our graph for the function F and one of the points we were given is the 10.4 comma 10. That means that four or sorry F evaluated at four is equal to 10. And when we have an X value of four, we get an F of X value of 10. So now we're gonna have G evaluated at 10. This, we know how to do. We go to our graph for G, we look for an X value of 10 and we see with the points we were given and based on the graph that, that corresponds with the G value of seven, OK, an X value of 10 A Y value of 70. And so G at 10 is equal to 70. So we weren't given the composite function itself but having information about F and having information about G on their own was enough to evaluate them at four. We found that the correct answer is 70 which corresponds with answer choice B Thanks everyone for watching. I hope this video helped see you in the next one.

The graphs of two functions ƒ and g are shown in the figures.
Find (g∘ƒ)(3).

Key Concepts

Function Composition

Evaluating Functions

Graph Interpretation

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