Let

Question

Let

ƒ (x) = x^{2} + 3

and

g (x) = - 2 x + 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 function to find the given composite function. So what we are asked to find is F times G of negative eight. But before we find this composite function, we need to find the general form of the composite function which is going to be F times G of X. Now F times G of X can be written as F of X times G of X. And what this means is we're going to be taking our given F of X function and multiplying it with the given G of X function and replacing F of X and G of X with the giving functions is going to give us the quantities two X squared plus one times negative five X plus two. And this is going to be the general form of the given composite function that we're looking for. Now, let's go ahead and find the composite function with the given input value. So F times G of negative eight can be rewritten as F of negative eight times G of negative eight. And that means that we're going to take the products of the two functions. But with eight as its input value. So plugging in negative eight into the input values is going to give us two times negative eight squared Plus one times the quantity negative five times negative eight plus two. And now we need to go ahead and simplify in the left group, negative eight squared is going to give us 64. So we have two times 64 plus one and on the right group negative five times negative eight is going to give us positive 40. So we have 40 plus two. Now two times 64 plus one is going to give us the value of 129 and 40 plus two is going to give us 42. So what we are left with is 100 and 29 times 42 which is going to give us a final value of 5418. And this is going to be the value of the given composite function F times G of negative eight. 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.

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

Key Concepts

Function Composition

Evaluating Functions at a Given Input

Polynomial and Linear Functions

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