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 are asked to find F times G and then 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. So in order to find F times G, what we are going to do is take our given F of X function and multiply our given G of X function to it. That's going to be the square root of x minus 17 times the square root of 17 minus X. And this is going to be the function F times G. Now we need to go ahead and write its domain. Well if you notice x minus 17 and 17 minus X are negative congruence of each other. So we can go ahead and take X minus 17 and set it equal to 17 minus X. And once we solve for X, this is going to give us the value of X. That works with this function so we can go ahead and add X to both sides of this equation and add 17 to both sides. Doing so is going to give me two. X is equal to 34. Now, finally, I just need to go ahead and divide both sides by two and I get X is equal to 17 and this is going to be our domain because this is the only value of X that allows this function to work. So just to reiterate F times G is equal to the square root of x minus 17 times the square root of 17 minus X, and its domain is X is equal to 17. So 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.

Struggling with College Algebra?

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)

Watch next

Function Operations practice set