In Exercises 1–30, find the domain of each function. f(x) = 1/[3/...

Question

In Exercises 1–30, find the domain of each function. f(x) = 1/[3/(x - 1) - 2]

Accepted Answer

So this problem says for the given function find the domain our equation F of x equals 16/8 over two X minus two. I first want to simplify the equation a little bit. So if you look here By then we have an 8/2 x. That will go to four over X minus two. Now we can go even farther. If you notice here, everything can have a two taken out. So I rewrite it again. two times 8 for 16 over to that's two over X minus what we can divide out our twos, meaning our most simple form of this equation is 8/2 over x minus one. Now is the final domain of this equation, we just set our denominator equal to zero. That will give us any undefined values of our equation. So Let's go ahead and find the domain. We're gonna set two over X -1 equal to zero. Let's go ahead and solve for X. We add one here, add one. We get two over X equals one. I will divide. Actually multiply both sides by X. Get us two equals x. So one of our variables cannot be equal to two, then X rather cannot be equal to two. We also have to keep in mind that we have a two over X here as well. Well, domain of two over X. We set that equal to zero. We can tell that X cannot be equal to zero, meaning that we have two places where our function is discontinuous at X equals zero and X equals two. So those cannot be equal right at our domain. You will have all real numbers except for X0 and X is two. So Nate infinity to zero and 0 to 2, and 2 to infinity will give us all the numbers we can have on this domain, meaning the answer to our domain. His answer is C. Okay. I hope to help you solve the problem. Thank you for watching. Goodbye.

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