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)(3)

Accepted Answer

Hello, today we're going to be using the given F of X and G of X functions to find the following composite function. So what we are given is to find F plus G of six. But before we find this composite function, we need to find the general form of the composite function which is F plus G of X. Now F plus G of X can be rewritten as F of X plus G of X. And what this means is we're going to be taking the sum of our given F of X and G of X functions. So replacing F of X and G of X with the given functions is going to give us two X squared plus one plus the quantity negative five X plus two. And now we can go ahead and do a little simplification, we can add negative one and two together and plus negative five X is going to give us negative five X. So what we are left with is two X squared minus five X plus three. And this is going to be the general form of the composite function that we are looking for. Now, we want to go ahead and find the value of the composite function with six as its input value. And what this means is we're going to be taking the value of six and replacing every X in our composite function with that value doing this is going to give us the function two times six squared -5 times six Plus three. And now we just need to go ahead and simplify Six squared is going to give us 36 and 36 times two is going to give us the value of 72 negative five times six is going to give us negative 30. And what we are left with is plus three. So 72 minus 30 plus three is going to give us the value of 45 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 be. 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.

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

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