For the pair of functions defined, find (ƒg)(x). Give the doma...

Question

For the pair of functions defined, find (ƒg)(x). Give the domain of each. See Example 2.

ƒ(x)=2x^2-3x, g(x)=x^2-x+3

Accepted Answer

Hello everyone. We're going to find the function for F times G. Of X. When we are given the function F. Of X equals four X squared minus two X. And G. Of X equals X squared minus five X plus seven. Then we're going to determine what their domain is. So I'm going to set this up so I have the two functions multiplied times each other. So F. Of X. I'm going to put in parentheses and do four X squared minus two X times my next set of parentheses which is my G. Of X. So X squared -5 x plus seven. Now looks like all I can do is multiply. So I'm going to distribute from my binomial into my try no meal. So I have four X squared times X. Squared which gives me four X to the fourth. And then I'm gonna go four X squared times negative five X. So negative 20 X to the third. Four X squared times seven. So plus 28 X squared. And then the next term I'm gonna treat this as a negative two X negative two X. Times X squared is negative two X to the third. Negative two X times minus five X. Would give me a positive 10 X squared and negative two X. Times seven gives me negative 14 X. All right so I want to combine my like terms I have no other X to the fourth. So I'm gonna leave for X to the fourth. I have a negative 20 X to the third and a negative two X to the third to give me negative 22 X to the third, I have a 28 X squared and a 10 X squared. So plus 38 X squared And then -14 x. So there are no more like terms. So this is the function that is our solution. It's four X to the fourth minus 22 X to the third plus 38 X squared minus 14 X. But we still need to decide what the domain is. So the domain of my original F of X. Because it doesn't have any radicals or fractions is all real numbers. The domain of my original G of X is the same. It has no radical, no fraction. So it's still all real numbers. And my new function has no radical has no fraction. So our domain here for F times G of X, the domain is still gonna be all real numbers. So negative infinity. To positive infinity. So our answer choice is answer choice. A. Have a nice day.

For the pair of functions defined, find (ƒg)(x). Give the domain of each. See Example 2.
ƒ(x)=2x^2-3x, g(x)=x^2-x+3

Key Concepts

Function Composition

Domain of a Function

Polynomial Functions

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