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 -5, g(x) = 3x²

Accepted Answer

this problem says for the given functions F X equals x minus seven and G X equals seven X squared. Find F over G. And domain. So let's go ahead and find F over G. So F over G. Now F is our first equation X minus seven. And G is our second equation seven X squared. I want to see if we can simplify this or looking at this. We have an expanded seven top. There's not really anything. We can cancel it on the bottom. So we're gonna leave our equation just like this. Now I want to find out what the domain that this equation is. You know, So we have a rational function but we have a denominator that is polynomial. So to determine our domain, we need to see what will make the denominator of this fraction zero because we can't have a division by zero. It just doesn't work because undefined. So we want to check to see what's going to make this denominator equal to zero. So we can take our seven X squared and bring it outside. Just temporarily Set it equal to zero. Let's figure out what number will make this equal to zero. We can divide by seven on both sides to get X squared equals zero. And finally the square root you get X equals zero. So at X equals zero. We're going to get an undefined meaning that our domain is all real numbers except for where X is equal to zero. So We said x nickel zero. This turns the domain negative infinity. 20 and zero to infinity. That is all real numbers, except for zero with our equation being x minus 7/7 X squared. So the answer to our equation as answers. Okay, I hope that we 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 -5, g(x) = 3x²

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