Domain of Rational Number

[harpazo]

Find domain of g(t) = 5t/(t^3 - 16t).

Solution:

Set denominator equal to 0 and solve for t.

t^3 - 16t

t(t^2 - 16)

t(t - 4)(t + 4) = 0

t = 0, t = -4, t = 4.

Let d = domain

d = {t | t = all real numbers except that t cannot be 0, -4 and 4}.

Interval Notation

(-00, -4) U (-4, 0) U (0, 4) U (4, 00)

Is this right?

Note: -00 = negative infinity, 00 = positive infinity in my interval notation.

 

[Harry_the_cat]

Yes

 

[HallsofIvy]

Yes, that is correct. Well done!

 

[harpazo]

Wonderful. Another question for my math files.

 

[HallsofIvy]

But why was this titled "domain of all rational numbers"? The domain does NOT include all rational number and many numbers that are not rational.

 

[harpazo]

But why was this titled "domain of all rational numbers"? The domain does NOT include all rational number and many numbers that are not rational.

Typo at my end.

 

[HallsofIvy]

Oh, I nefer make mistakes like that!

 

[harpazo]

Oh, I nefer make mistakes like that!

It's not a big deal.

 

[Dr.Peterson]

I'm guessing the intended title was "Domain of a Rational Function". I wouldn't call it a typo, but it's a slip I've probably made more than once.

On the other hand, to read "Domain of Rational Number" as "Domain of all rational numbers" is also an error, presumably caused by seeing what one expects. I suspect we're all human here.

 

[harpazo]

I'm guessing the intended title was "Domain of a Rational Function". I wouldn't call it a typo, but it's a slip I've probably made more than once.

On the other hand, to read "Domain of Rational Number" as "Domain of all rational numbers" is also an error, presumably caused by seeing what one expects. I suspect we're all human here.

We all make mistake.