A-Level Maths: B8-15 Functions: Domain and Range of an Inverse Function

[@leonardowilhelmdicaprio999]

Thank you so much!This is exactly what I needed.I'll admit that I've always never understood this topic well but all that changed upon watching this video.Everything's so well explained.

[@Suzan557]

All your videos on functions have made the topic so much easier. I love how in the first video on functions you go way back to the function machines. That really helped me understand functions so much better. Thank you

[@jess8370]

hi jack! i just want to say a big THANK YOU for making all those AMAZING math videos on your youtube channel. i’m so thankful to have them, for without them i would be struggling through AMath. your videos help me grasp math concepts better with as you make sure everything is explained clearly and concisely. i am also heartened to see that you never fail to reply to people’s queries in the comments section. please never give up on this and continue to make such AMAZING videos!! God bless you 🙏❤️

[@TLMaths]

Thank you!

[@knowledgeispower6949]

This guy is so easy to follow. Thanks 😊

[@GCSEALevelMaths2025]

Very useful and clear and coherent!! Thank you very much for this sir!! Thanks!!

[@YathinJP]

Just started this topic yeet

[@hisschoolwork3987]

Hi Jack! Thanks so much for your videos, they're already helping me two weeks into maths/further maths a level. I just have one quick question : do you recommend I buy the Casio 991-ex or rather the graphical calculator (CG50), considering I'm taking both a level maths and further maths? I was just wondering if you had an opinion or recommendation. Thanks :D

[@TLMaths]

Personally, I've never had the need for a graphical calculator - I'd stick with the casio classwiz. For FM, you may find use for the graphical with polar curves - just depends how confident you are

[@hisschoolwork3987]

@@TLMaths Thank you :DDD

[@leonardowilhelmdicaprio999]

@@TLMaths Is the Casio ClassWiz a programmable calculator?

[@TLMaths]

No

[@saadsyed9838]

Someone help me with this question. Give the range of k values, for which the quadratic equation z²-kz+2k = 0 has non-real roots. k is an element of the real numbers. Thx Thx

[@TLMaths]

No real roots implies that the discriminant is negative (-k)^2 - 4*1*(2k) < 0 k^2 -8k < 0 k(k - 8) < 0 Draw a sketch of a parabola passing through 0 and 8 on the "k-axis", and ask: where is the parabola BELOW the k-axis? So the solution is 0 < k < 8 www.desmos.com/calculator/eya1k5hlst

[@Yleano]

Do you give private lessons online or have you ever considered doing so? I am an Spanish who came to Uk, and after some years working as a music teacher I am thinking of doing something different. I am going to take A levels (I did bachiller in Spain, kind of equivalent) but I am studying by myself which I sometimes found tricky. I am using your videos because I found them very helpful, but if you consider to give online lessons, I would be very happy to pay you for that. No pressure 😊

[@TLMaths]

Unfortunately I don't currently offer private tuition - I've got far too much on my plate to juggle at the moment. Glad you're finding the videos useful!

[@Yleano]

@@TLMaths what a shame, but I understand. Actually, that's what I thought... But I had to ask 🙂. Your videos are great, everything is clear... And I can understand them, which is something I struggle with often as English is not my main language. Great job, thanks a lot.

[@forthrightgambitia1032]

Is it required to graph it? Working it out it algebraically seems like it would be a lot less hassle.

[@TLMaths]

Less hassle and full marks don't always go hand in hand unfortunately. You must be prepared for anything.

[@CamMathsTutor]

Nice!👍

[@jess8370]

i have a question - all inverse graphs only meet at one point that is on the y=x is that true?

[@TLMaths]

No this isn't the case. f(x) = x^3 and f^-1(x) = x^(1/3) meet at three points on the y=x line: www.desmos.com/calculator/4apvgawomb

[@alexmitchell4374]

Hi Jack, it says on the AQA website that Paper 1 is Pure, Paper 2 is Mechanics and Paper 3 is Stats. I thought it was P1 - P, P2 - P/M, P3 - P/S

[@TLMaths]

Yes, it is as you say. Can you send me the link?

[@babajani3569]

Hello sir. I am sorry if this sounds like a stupid question but I dont understand why when coordinates (a,b) are reflected in y=x then those coordinates will become (b,a). Secondly, how do you know this will always be true. Thank you.

[@TLMaths]

Here are a couple of points to help you visualise it: www.desmos.com/calculator/j8ogiofiyy

[@leerock1028]

thank you very much

[@redroses4679]

How do we know the range includes -8 , but not 8? For f(x)

[@TLMaths]

3 is not included in the domain, so 8 can't be included in the range.