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

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

50 Comments

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

    Youโ€™re amazing thanks for sharing!!!! Your breakdown of math concepts is phenomenal.



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

    Wait a sec…
    Is she writing backwards ๐Ÿคจ?



  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

    Op ๐Ÿ˜Ž



  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



  13. 2040 __เคชเฅเคฐเคœเฅเคฏเฅ‹เคค เค˜เคพเคกเค—เฅ‡ on August 12, 2021 at 9:30 pm

    Nancy๐Ÿค—๐Ÿฅฐ



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

    You are very nice when comes to solve problems big up



  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

    You are awesome. Thanks



  22. Thomas Uga on August 12, 2021 at 9:41 pm

    Sheโ€™s hot



  23. FITSUM AMSALU on August 12, 2021 at 9:43 pm

    I want to say thank you



  24. Vanessa R. Hove on August 12, 2021 at 9:43 pm

    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.



  26. MemeX on August 12, 2021 at 9:44 pm

    .



  27. แŽ 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 = ? ..



  28. ็ฅžๆตท on August 12, 2021 at 9:45 pm

    Thank you for the clear explanation!



  29. Mari. G on August 12, 2021 at 9:45 pm

    why didnt u add ‘R’ at 11:39?



  30. Zeeshan Sami Sami on August 12, 2021 at 9:45 pm

    Thanks โ˜บ๏ธ๐Ÿ‘โ˜บ๏ธโค๏ธ



  31. Rida Saleem on August 12, 2021 at 9:46 pm

    I have checked a lot of lectures but unable to understand this topic..But you made it simple๐Ÿคฉ ..Your way of teaching is impressive..
    God bless you๐Ÿ˜Š



  32. Catrina on August 12, 2021 at 9:48 pm

    Why you donot make videos now in 2021?



  33. Mary Zulu on August 12, 2021 at 9:49 pm

    She is good



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

    nancy, do you have a video on range??



  36. NAYEEN STATUS on August 12, 2021 at 9:51 pm

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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?



  42. Marzia Rangel on August 12, 2021 at 10:05 pm

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  44. Mari. G on August 12, 2021 at 10:09 pm

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  46. walter tono on August 12, 2021 at 10:09 pm

    THANK U



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

    Thank you . Can we about range too?



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