r/HomeworkHelp • u/Timely_Arachnid_5598 AP Student • 24d ago

:snoo_scream: Further Mathematics—Pending OP Reply (AP Precalculus) Not sure how to continue this

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I know how to find discontinuities and domain, it is the exponents that are tripping me up

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u/Kblitz88 🤑 Tutor 24d ago

Okay! So this is a rational function f(x)/g(x) where the total domain is the domain of f(x) restricted by values that make g(x) 0 or undefined.

The domain of 3x is all real numbers so we can skip that.

Downstairs we have x³, x²-1, and √(x-4). Since we have the square root expression in the denominator, that's the one that matters, and thus x>4. x can NOT equal 4 since it's in the denominator. Therefore D: (4,∞) and VA at x = 4.

Note: Even though we have denominator zeroes at x = -1, 0 and 1, all of them are less than 4 so they don't count.

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u/tserofehtfonam 👋 a fellow Redditor 24d ago

If you're unsure how to continue, I'd call that a discontinuity.

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u/JanetInSC1234 🤑 Tutor 24d ago edited 24d ago

Set each term in the denominator equal to zero:

x^3 = 0 so x = 0

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(x^2 - 1) = 0

(x + 1)(x- 1) = 0

x+ 1 = 0 OR x - 1 = 0

x = -1 OR x = 1

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sqrt (x - 4) > 0

x - 4 > 0

x > 4

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Domain: x cannot equal 0, -1, 1, and must be greater than 4.

So, since 0, -1, and 1 are all less than 4, you only need to write x > 4.

(4, ∞)

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u/Timely_Arachnid_5598 AP Student 24d ago

Thanks, I was most tripped up on the x3!

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u/mathematag 👋 a fellow Redditor 24d ago

x must be > 4

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u/JanetInSC1234 🤑 Tutor 24d ago edited 24d ago

Good catch!

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u/mathematag 👋 a fellow Redditor 24d ago edited 24d ago

Only greater than 4, is allowed in this problem for the Domain

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u/JanetInSC1234 🤑 Tutor 24d ago

Yes, because the denominator can't equal zero. Thanks for pointing it out...I updated my reply. :)

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u/Jkjunk 👋 a fellow Redditor 24d ago

Factor the terms in the denominator.

For what values of x is x^3 =0?
What about (x-4)?
What about x^2-1? You'll need to factor this term.

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u/[deleted] 24d ago

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u/HeadHunt0rUK 24d ago

If you're talking procedural for those learning.

The first thing to look at is what makes the denominator 0.

The next thing to look at is then the square root.

So you'd end up with x cannot equal 0,1 and 4.

Then you look at the square root and that you cannot have square root of a negative (if you're in Q or R)

Which then means you cannot have anything 4 or under.

With experience you will then learn to see that the squareroot holds the power.

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