Find a. (fog) (x) b. the domain of f o g.
f(x) = √x, g(...

Question

Find a. (fog) (x) b. the domain of f o g.

f(x) = √x, g(x) = x − 2

Accepted Answer

So this problem says that solved G f F of X. And also find the domain of G F F of X where F of X equals to X the third minus two and G X equals X squared plus six X. So I'm gonna first to write G F F X G F of X. This is the same thing as saying G on the outside F of X on the inside like this. So if we direct this even further, this just means we have G X 3 -2. Now everywhere where there's an X. And our G equation we're gonna instead plug in X the third minus two. So if you look here we have X squared plus six X. So instead we say X the third minus two squared A six times x the third minus two. Now I can simplify this a little bit. Don't go here. We have X the third minus two squared if I write this out and then over here we have six times X the third minus two. So that would be plus six X third minus 12. Waste on the factor these numbers here are foiled these numbers rather so X the third times X the third That is X the 6th Extra 3rd since native to is native to extra 3rd negative two times X two thirds negative two X the third and negative two times negative two is positive four. And we'll just bring down our plus six X to the third and our negative 12. Now we can combine like terms we only have one X to the sixth. So that stays there. We have a negative two X. The third minus two X to the third and plus six X. Third. We add all those together. We get native to minus two plus six which goes to plus two X to the third. Finally we have a positive 4 -12. That gives us -8. So our equation is X. The six plus two X. The third minus eight. We want to find a domain of this equation. However this is a polynomial and we don't have any restrictions on this type of polynomial. We have a polynomial to the sixth degree. So since we don't have any restrictions, this domain is all real numbers negative infinity to infinity. So that is our equation and this is our domain. Making art answer answer. C. Okay I hope to help you solve the problem. Thank you for watching. Goodbye.

Find a. (fog) (x) b. the domain of f o g.
f(x) = √x, g(x) = x − 2

Key Concepts

Function Composition

Domain of a Function

Square Root Function

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