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

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

Follow Nancy on Instagram! https://instagram.com/nancypi

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

1. Brittney Rain on August 12, 2021 at 9:17 pm

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2. Iruoghene Emeyoma-Atigbi on August 12, 2021 at 9:19 pm

Wait a sec…
Is she writing backwards ๐คจ?

3. Vigz McHardthrust on August 12, 2021 at 9:20 pm

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?

4. edward chanda on August 12, 2021 at 9:21 pm

Wow

5. Rishu on August 12, 2021 at 9:25 pm

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6. Thanawan Greaves on August 12, 2021 at 9:25 pm

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)

7. someone you don't know on August 12, 2021 at 9:25 pm

thanks a lot this is exactly what I needed

8. wolverine yt on August 12, 2021 at 9:26 pm

thank yu nancy

9. Jim Jim on August 12, 2021 at 9:29 pm

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

10. Guru Puduru on August 12, 2021 at 9:29 pm

Thx

11. Mari. G on August 12, 2021 at 9:29 pm

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?

12. Joolfoo Munir on August 12, 2021 at 9:29 pm

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

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14. karim kaunda on August 12, 2021 at 9:31 pm

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15. Ayo on August 12, 2021 at 9:33 pm

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

16. M.F. Husain on August 12, 2021 at 9:37 pm

Well explained

17. Dhruv Narayan Mishra on August 12, 2021 at 9:38 pm

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

18. alexa bianco on August 12, 2021 at 9:38 pm

i wish she was my calc teacher

19. Wooowww Cranchy!!! on August 12, 2021 at 9:39 pm

thanks for saving my math grade lmaooo

20. Melanie on August 12, 2021 at 9:40 pm

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

21. Adama Jarju on August 12, 2021 at 9:41 pm

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I want to say thank you

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You are the best there is

25. Ivy on August 12, 2021 at 9:43 pm

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

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.

27. แ ฤีพีชษพาฝฤสส on August 12, 2021 at 9:44 pm

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

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Thank you for the clear explanation!

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why didnt u add ‘R’ at 11:39?

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God bless you๐

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35. Jasjeet Singh on August 12, 2021 at 9:51 pm

nancy, do you have a video on range??

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37. alittA X on August 12, 2021 at 9:52 pm

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.

38. parmilsharma sharma on August 12, 2021 at 9:52 pm

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

39. Tabitha Pascual on August 12, 2021 at 9:52 pm

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.

40. AVEC VICKEYS on August 12, 2021 at 9:53 pm

Thank you

41. Mr. Lerma on August 12, 2021 at 10:05 pm

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?

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47. Aashwasan Dahal on August 12, 2021 at 10:11 pm

Thank you . Can we about range too?

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50. Abdoulie Janneh on August 12, 2021 at 10:15 pm

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