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 g(x) with points (1,-6) and (5,10) marked, for function operations.

Find (ƒ∘g)(2).

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 given is the composition function F of G evaluated at one. The graphs were given, we have two of them. On the left hand side, we have the graph of G of X. Hey, this looks quadratic, we have a parabola opening upwards and we're giving two points on this graph. We're giving the 20.1 negative six and the 0. 10. On the right hand side, we have the graph of F of X. This looks like a straight line. OK. It has a positive slope. And again, we're given two points negative six, negative one and 0 23. We're given four answer choices, option A one, option B negative one, option C negative six and option D six, we're gonna start by rewriting the expression we were given. So we have the composition function F of G and we wanna evaluate this at one. Now, we aren't giving information about this composite function F of G. So how do we evaluate it at a particular point? OK. All we're given is information about G on its own. And information about F on its own from those graphs will recall that the composite function F of G evaluated at the 0. can be written as the function F evaluated at the function G evaluated at one. All right. So we've rewritten this. How can we actually evaluate, well, we can't evaluate the odor function yet. OK. We have F evaluated at some function value that we don't know yet. So we can't evaluate that yet. But what we can do is start on the inside and work our way out. OK. So let's start by evaluating the function G at one. OK. This inside term. Now if we look at our graph for the function G, we look at an X value of one, we see that it has a corresponding Y value of negative six and we're given that 60.1 negative six. So G at one is equal to negative six. And so our expression becomes F at negative six, we know how to do this. We're just evaluating a particular function at a particular point. So we go to our graph of F, we look at an X value of negative six and we see that it corresponds with the Y value of negative one. OK. And again, we're given that point negative six negative one. So F evaluated at negative six is equal to negative one. So our composite function F of G evaluated at one is going to be equal to negative one. The correct answer matches with option B. That's it for this one. Thanks everyone for watching. See you in the next video.

The graphs of two functions ƒ and g are shown in the figures.
Find (ƒ∘g)(2).

Key Concepts

Function Composition

Evaluating Functions

Graph Interpretation

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