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 be finding the function F minus G. And then we're going to write its domain. So the given F of X function is f of X is equal to the square root of x minus 11. And the given G of X function is going to equal to the square root of 11 minus X. We want to go ahead and find f minus G. But what that means is we're going to take our given F of X function and we're going to subtract are given G of X function from that. So that's going to be the square root of x minus minus the square root of 11 minus X. And this is going to be our function f minus G. Now we need to go ahead and write its domain and there's only gonna be one possible number that allows this domain to work and that's going to be 11. Well, how do we know that though? X -11 and 11 -1 are negative congruence of each other. So we can go ahead and set X -11 equal to -X. And we need to go ahead and sell for X. I can go ahead and add X to both sides of the equation and add 11 to both sides of this equation. That's going to give me two. X is equal to 22 and then I can go ahead and divide both sides by two and that's going to give me X is equal to 11. So this is gonna be our domain because this is the only number of X that allows this equation to work. So that means that our function f minus G is going to be the square root of x minus 11 minus the square root of 11 minus X, and its domain is going to be X is equal to 11. So the answer to this problem is going to be D. 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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