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)(-1)

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 asked to find is F -G of -4. But before we find this composite function, we need to find the general form of the composite function which is F -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 we're going to be taking the given F of X function and subtracting it with the given G of X function. So replacing F of X and G of X with the given functions is going to give us two X squared plus one minus the quantity negative five X plus two. And just for a little simplification, we can distribute negative one into the quantity negative five X plus two. And this is going to give us two X squared plus one plus five X minus two. Now we can go ahead and combine like terms by adding one and negative two together. And that's going to give us two X squared plus five X minus one, which is going to be the general form of our composite function. Now, we want to go ahead and find the value of the composite function with negative four as the input value. So what this means is we're going to be taking negative four and replacing every X in our composite function with that value. And that's going to give us two times negative four squared Plus five times -4 -1. And now we just need to go ahead and simplify negative four squared is going to give us 16 and 16 times two is going to give us 32 five times negative four is going to give us negative 20 and we have minus one as the constant And 32 -20 -1 is going to give us the value of positive 11, which is going to be the value of the given composite function we are looking for. And with that being said, the answer to this problem is going to be C 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)(-1)

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