In Exercises 31–50, find ƒ+g, f−g, fg, and f/g. Determine the dom...

Question

In Exercises 31–50, find ƒ+g, f−g, fg, and f/g. Determine the domain for each function. f(x) = √(x -2), g(x) = √(2-x)

Accepted Answer

Hello. Today we're going to find the function F over G and write its domain. So the given F of X function is F of X is equal to the square root of x minus 17. And the given G of X function is the square root of 17 minus X. We need to go ahead and find F over G. And that F over G means is that we're going to take our given F of X and divided by our given G of X. So that's going to be the square root of X - over the square root of 17 -1. And this is going to be the function f over G. Now we need to go ahead and find its domain. Well, notice that X minus 17 and 17 minus X are negative congruence of each other. So we can go ahead and set x minus 17 equal to 17 minus X and solve for X. So I can go ahead and add X to both sides of the equation and add to both sides of the equation. That's going to give me two, X is equal to 34. And if I divide both sides by two, X is going to equal to 17. Now, this is a possible value for the domain but this value of X does not work with our given function because if we were to plug 17 into our F over G function, we get 0/0, which is undetermined. So that means that the domain is going to be the set No, because there are no possible values of X that allow this function to work. So F over G is equal to the square root of x minus 17 over the square root of 17 minus x. And the domain is the set No. With that being said, the answer to this problem is going to be a So I hope this video helps you in understanding how to solve this type of problem, and I'll go ahead and see you all in the next video.

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In Exercises 31–50, find ƒ+g, f−g, fg, and f/g. Determine the domain for each function. f(x) = √(x -2), g(x) = √(2-x)

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