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How would I find the domain of f(x)=(x-1)/(x^2+1)

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- Thread starter UrbanXrisis
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- #1

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How would I find the domain of f(x)=(x-1)/(x^2+1)

- #2

Pyrrhus

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In your sample, you should do x^2 + 1 =0 so, x^2 = -1 and x = sqrt(-1), so that will be x = i, so an imaginary number will make it 0, that's great so this means the domain will be all the real numbers, because no real number can make it 0.

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what if the denominator had a sqrt such as sqrt(x-2)/(x^2-x)

- #4

Pyrrhus

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what if the denominator had a sqrt such as sqrt(x-2)/(x^2-x)

I will assume the following:

sqrt(x-2)/sqrt(x^2-x) well factoring the deniminator

sqrt(x-2)/sqrt(x(x-1)), read above what i said about the denominator.

Now this is a little addon:

take for example the numerator sqrt(x-2), if you had a value like x=2, it will make it 0 right? what about if you had a value like x=1 wouldn't that make it sqrt(-1), whoa, so now it has gone out of the real numbers into the imaginary numbers... and a value below 2 will put it into imaginary numbers..., so what should the restriction be? obviously x>=2.

Now try to find the domain for this.

- #5

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UrbanXrisis said:what if the denominator had a sqrt such as sqrt(x-2)/(x^2-x)

Same idea; solve the denominator for 0. The domain is all those values that don't make it 0

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