Let ƒ(x)=x^2+3 and g(x)=-2x+6. Find each of the following. See Ex...

Question

Let ƒ(x)=x^2+3 and g(x)=-2x+6. Find each of the following. See Example 1. (ƒ-g)(4)

Accepted Answer

Hello, today we're going to be using to give an F of X and G of X function to find the following composite function. So what we are asked to find is F -G of two. Now, before we find this composite function, we need to find the general form of the composite function which is F minus G of X. Now F minus G of X can be rewritten as F of X minus G of X. And what this means is that we're going to be taking the given F of X function and subtracting it with the given G of X function and plugging into two given functions is going to give us two X squared plus one minus the quantity negative five X plus two. Now, just to simplify this, we're gonna go ahead and distribute negative one into the quantity negative five X plus two. And that's going to give us two X squared plus one plus five X minus two. And now we can go ahead and combine like terms which is negative two and positive one. And that's going to give us two X squared plus five X minus one. And this is going to be the general form of our current composite function. Now, what we want to do is find the value of the composite function with negative two as its input. So again, F -G of two can be written as f of two -G of two. So we're gonna be replacing every X R composite function with the value of positive two. And that's going to give us two times two squared Plus five times minus one. And just to do a little simplification, two squared is going to give us four and four times two, gives us the value of eight, Five times two is going to give us 10. And what we're left with is -1 with the constant And 8-plus 10 -1 is going to give us the value of 17, which is going to be the value of the composite function that we are looking for. 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.

Let ƒ(x)=x^2+3 and g(x)=-2x+6. Find each of the following. See Example 1. (ƒ-g)(4)

Key Concepts

Function Notation

Function Operations

Evaluating Functions

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