In Exercises 31–50, find fg and determine the domain for each fun...

Question

In Exercises 31–50, find fg and determine the domain for each function. f(x) = 2x + 3, g(x) = x − 1

Accepted Answer

So this problem says for the given functions F x equals five X plus 12 and G X equals x minus +65 F times G. And write the domain. So its first final F times G is F times G. That's equal to our first expression five X plus times our second expression x minus six. I'm gonna multiply these two expressions together to do that. We will make use of the foil technique oil techniques states that we multiply our first terms and expressions together. Then we add the multiplication of our outer terms of our questions plus the multiplication of the middle terms and plus our last terms. So we write that out, we first get five x times x which gives us five X square get our outer terms as five X times negative six which is negative 30 X. And inner terms 12 times X which is 12 X. And finally our last terms of 12 times negative six which is negative 72. We simplified it further. We have five X squared combining our middle terms. We will get minus 18 X And -72. Now we want to check the domain of this function. Check it out man. We want to see if there is a restriction. Usually restriction is given by a denominator with the polynomial or a square root. We look here, we don't have a denominator to our equation and we don't have a square root anywhere in our equation. Since that is the case our domain is going to be from negative infinity to infinity or all real numbers. Amen. And our equation five x squared minus 18 x minus are given and answer a okay, I hope that we solve the problem. Thank you for watching. Goodbye.

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