More composite functions Let ƒ(x)...

Question

More composite functions Let ƒ(x) = | x | , g(x)= x² - 4 , F(x) = √x , G(x) = (1)/(x-2) Determine the following composite functions and give their domains.

ƒ o g

Accepted Answer

Hello. Today we're going to be using the following functions to find the composite function and its domain. So we are told that the a of x function is equal to the absolute value of x minus 2. We are also told that the b of x function is equal to 2 x squared plus 7. We want to use these two functions to find the composite function a of b of x. So how can we start finding this composite function? Well, to make things a little easier to read, we can rewrite the notation of the composite function as a of b of x. What this means is that the composite function will the composite function we're looking for will be the function b of x plugged into the function a of x. So what this means is that for every variable x within the a of x function, we're going to be replacing that variable with the b of x function. So if we follow this, the a, the composite function is going to be the absolute value of 2x squared+7-two. Now we have one step to simplify this function. If we add the constants 7 and negative 2, what we are left with is 2 x squared+5. This is going to be the simplest form of the composite function a of b of x. Now that we have the composite function, we want to find the domain. Now, the absolute value function can be considered a polynomial, and the domain of any polynomial is all real numbers, or in other words, can be written as negative infinity to positive infinity. This will be the domain of our 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.

More composite functions Let ƒ(x) = | x | , g(x)= x² - 4 , F(x) = √x , G(x) = (1)/(x-2) Determine the following composite functions and give their domains.

ƒ o g

Key Concepts

Composite Functions

Domain of a Function

Absolute Value Function

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