In Exercises 67-74, find
a. (fog) (x)
b. the domain of f o g.
f(...

Question

In Exercises 67-74, find
a. (fog) (x)
b. the domain of f o g. 
f(x) = x/(x+1), g(x) = 4/x

Accepted Answer

So this problem says the solved G f F of X. And also find a domain of G F F of X where f of X equals a squared of X plus two X. And G F X is X squared minus two. Let's go ahead and write this out. Look here we have G F F of X. This means that we have G on the outside. Can we have F of X on the inside? So if we rewrite this we're gonna take G. And just everywhere where there's an X. We're gonna replace it with a five X. So we have squared of X plus two X. No, we have to rewrite the skin. Look here we have X squared minus two everywhere. There's an X. We will write our F of X. We have squared of X plus two X squared minus two. So now we're going to simplify this equation even further. So G f X that is going to be squared of X plus two X times squared of X plus two X minus two, certify this will foil. So we'll take our first terms multiply them, our outer terms multiply them. And our last terms. So we will get squared of X times the square root of X which is just X squared of X times two. X is two X squared of X in the middle. We have to expletive X again and finally we have two X times two X which is four X squared. And to bring down our minus two. Now we can combine like terms. So I'm gonna move my four X squared to the front just for order sake we have four X squared. Then we have two X plus two X. They're both multiplied by the square root of X, add those together. We get four X squared of X. We bring down our X because of nothing to combine and we bring down our -2. So this is the equation or R G f f f f X. Now we need to find the domain of this equation. You look here we have a four X squared here. The domain of a polynomial is all real numbers. So domain of X squared would be all real numbers the same for X. However we do have a squared of X here not a squared of X. That domain is from zero to infinity. That is because we can't have a negative square root. So so we have squared of negative one. That does not work does not work. So our domain for the sport of X is 0 to infinity. Now because that is inside the entire function we have to go by the rules of the squared of X. Are german is from zero to infinity. So that's our domain and this is our equation. The answer to our problem is answer a Okay I hope to help you solve the problem. Thank you for watching. Goodbye

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