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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Hello, today we're gonna be using the given F of X and G of X function to find the following composite function. So what we are asked to find is F divided by G of -4. And before we find this composite function, we need to find the general form of the composite function which is going to be F divided by G of X. Now F divided by G of X can be rewritten as F of X divided by G of X. And what this means is that we're going to take our given F of X function and divided by the given G of X function. And that's going to give us the composite function two X squared plus one divided by negative five, X plus two. So what we have right here is the general form of the composite function F divided by G of negative four. But now let's go ahead and find the composite function with negative four as the input value. So F divided by G of negative four can be written as F of negative four divided by G of negative four. And we're gonna go ahead and plug in negative four into our general form of the composite function. And that's going to give us two times negative four squared plus one in the numerator divided by negative five times negative four in the denominator plus two. And now we just need to go ahead and simplify in the numerator negative four squared is going to give us 16. So we have two times 16 plus one. And in the denominator negative five times negative four is going to give us positive 20. So we have 20 plus two. Now in the numerator two times 16 plus one is going to give us 33. And in the denominator 20-plus 2 is going to give us 22. So the current value for F of G of negative or F divided by G of negative four is equal to 33 divided by 22. But we can further simplify this value because both the numerator and denominator are divisible by 11. So if we divide the numerator and denominator by 11, we get the fraction 3/2, which is going to be the value of the given composite function. 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)(-1)

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Key Concepts

Function Notation

Division of Functions

Evaluating Functions