In Exercises 31–50, find f/g and determine the domain for each fu...

Question

In Exercises 31–50, find f/g and determine the domain for each function. f(x) = √x, g(x) = x − 4

Accepted Answer

for the given functions F. X equals the square root of three X. And G. X equals six X plus seven. Find F divided by G. And record domain. Let's go ahead and write F divided by G. So we have F Over G. The equation for F. We have the square root of three X. G. X. Is six X plus seven. If you look here we can't really simplify anything. So we're gonna leave this as our function. Now. Let's go ahead and check the domain to check the domain. We want to see if anything is going to restrict our X in our way. In other words, if we plug in X values, they're going to give us an why that's not possible or imaginary or something like that. So I feel like here we have squared of three X. And it's divided by six X plus seven. The first check we could do is set the denominator. So detective denominator. We want to find any X. Value that's equal. That makes the whole thing equal to zero. On the bottom. Other words, let's set up the nominator. Six X plus seven equal to zero. Let's go ahead and solve for X. We would subtract seven first on both sides to get six X equals negative seven. And finally divided by six to get X equals negative 7/6. So one value. R. X can't be is negative 7/6. Let's check our numerator to see if that has any issues. So if you look at that we have a squirt of 3X. So this actually does have restriction because the square root function, a square root function cannot be negative. So if we had a negative X. That would not be a real answer. So we have a square of three x. Well let's go and solve for X. Three X equals zero. Will set everything under the square root equal to zero by by three X is equal to zero. Now in the school that we can't have any negative numbers. So anything that's going to be less than our X. Or result in the radical being negative. It's like if I were to plug in and X equals negative one for instance, I would get squared of three times negative one which is the square root of negative three which is no longer a real answer. So we want it's a B zero or greater which means the domain Of the squared of X is from 0 to infinity. So now we want to determine what our domain is. We said before that X cannot equal negative 7/6. But we also have to look at the domain of square the three X. Which means the domain has to be from zero to infinity. Well, negative 7/6 is less than zero. It's a negative number. So that answer is actually not going to matter in this case meaning our domain, it's just from zero to infinity With our equation. Now you have three x Over six X. Plus seven. The answer to this problem is answer D. Okay. I hope to help you solve the problem. Thank you for watching. Goodbye.

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In Exercises 31–50, find f/g and determine the domain for each function. f(x) = √x, g(x) = x − 4

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