# How to Find the Domain of Any Function (NancyPi)

How to Find the Domain of Any Function (NancyPi)

MIT grad shows a surefire way to find the domain of any function. To skip ahead: 1) For POLYNOMIAL only, skip to time 0:45. 2) For FRACTION only, skip to time 1:44. 3) For SQUARE ROOT only, skip to 5:08. 4) For SQUARE ROOT ON BOTTOM of Fraction, skip to 8:44. 5) For SQUARE ROOT ON TOP of Fraction, skip to 10:09. Nancy formerly of MathBFF explains the steps.

For how to SOLVE QUADRATIC equations by FACTORING, jump to: https://youtu.be/Z5MnP9da4EM

For how to SOLVE INEQUALITIES, jump to: https://youtu.be/ONuIIvgkE3c

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For Domain, you just need to watch out for Square Roots and/or Fractions!

If your function is…

1) a POLYNOMIAL (no square roots or fractions), i.e. f(x) = x^2 + 3x + 1, domain is “all real numbers.”

2) a FRACTION (w/ no square root), i.e. f(x) = (2x+1)/(x^2+5x+6). Set bottom “not equal” to zero. Solve for x.

3) a SQUARE ROOT (w/ no fraction), i.e. f(x) = sqrt(x+1). Set part under root “greater than or equal to zero”.

4) a FRACTION w/ A SQUARE ROOT ON BOTTOM, i.e. f(x) = (x^2+2x+3)/(sqrt(x+1)). Set part under root “greater than zero.” Solve the inequality. NOTE THE DIFFERENCE: You must set it greater than zero, not “greater than OR EQUAL TO zero” because we can’t have zero (or square root of zero) in the denominator.

5) a FRACTION w/ A SQUARE ROOT ON TOP, i.e. f(x) = (sqrt(x+1))/(x^2+4), i) Set the bottom “not equal to” zero & solve; ii) Set what’s under the root “greater than or equal to zero” & solve; iii) Take intersection of your two solutions.

For more of my math videos, check out: http://nancypi.com

Youโre amazing thanks for sharing!!!! Your breakdown of math concepts is phenomenal.

Wait a sec…

Is she writing backwards ๐คจ?

This was so very helpful but now I have a problem with a sqrt as both a root and bottom. f(x) = sqrt(x -6)/sqrt(x-4) . Which rule set do I use for that?

Wow

Op ๐

Awesome video! I don’t understand solving domain of f(x) = square root x2+5x+6. After fraction quadratic, why did you switch the sign of x to X<= -3, but sign for -2 still the same ( x>=-2)

thanks a lot this is exactly what I needed

thank yu nancy

At the 10:01 time mark, why isn’t there a bracket to include infinity?

Thx

at 7:49 how did u get less than or equal to -3 but not less than or equal to -3? both 3 and 2 had the same kind of equation in the beginning right?

I finally undestand ittt,Thanks but I get really sleepy hearing your voice LMAO

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You are very nice when comes to solve problems big up

Love this video, help me understand this much better. THanks

Well explained

What a beautiful idea of writing that is unique ………………..

i wish she was my calc teacher

thanks for saving my math grade lmaooo

What if the question is to find all values that are NOT in the domain?

You are awesome. Thanks

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I want to say thank you

You are the best there is

Nancy, you are so helpful. You’ve helped me so many times when nobody else made sense. Please keep making these wonderful videos.

.

Its too hard for my.. I need to learn the very basic 1 + 1 = ? ..

Thank you for the clear explanation!

why didnt u add ‘R’ at 11:39?

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I have checked a lot of lectures but unable to understand this topic..But you made it simple๐คฉ ..Your way of teaching is impressive..

God bless you๐

Why you donot make videos now in 2021?

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nancy, do you have a video on range??

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Can someone please explain the trick behind how she writes all letters perfectly even though she seems to be writing in a mirrored way? Thanks.

Please make a vedeo of finding range any function in which all type of functions are involve

In the section of Square root only second function, notice that this is an example of Quadratic Inequalities. The x should be less than or equal to -3. Imagine if you substitute the x with -4, (-4+3)(-4+2)>_ 0, the answer would be 2 and that is greater than 0, so the equation is till correct when x is less than -3. But x should not be greater than -3 and less than -2.

Thank you

This is 3 years late, but why is x^2 + 5X + 6 equal to -3 and -2? I got 3, 2 not negative. Did I miss something? Does the radical make them negative?

Thank you thank you thank you! So crystal clear ๐

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… a subject that i have been confused by for weeks cleared up in just 12 minutes… i applaud you ma’am

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THANK U

Thank you . Can we about range too?

Shit I can’t learn anything because of your beauty, can I get a personal lesson?….jkd

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Cheers ๐ฅ๐ฅ๐ฅ