You consider the range of g(x), as these values become the input values for fg(x) i.e. it's domain. You then consider this function's range. Hope that makes sense!
Hi sir! Just wondering for the last question, if needed in an exam or just in general, what would be the easiest way to sketch these types of graphs? I always find it difficult to find the horizontal asymptotes in comparison to the vertical ones, sometimes there is also more than one horizontal asymptote and it just trips me up
These kinds of graphs are actually very hard to sketch, and in an exam situation, I wouldn't confidently sketch this without my graphics calculator - you should make sure you can sketch the standard reciprocal type (1/x type). But this one is definitely more complicated! If you want to get better at graph sketching, there are probably some good TH-cam videos on it, but it is a very sophisticated topic that often comes up a lot in entrance exams for top universities!
It covers most, but definitely not all. It also doesn't really 'teach' all of these things, it is more designed to recap. So I would advise the playlist as your first approach, and then using these videos as a refresher! :)
Hi sir! I was wondering how do you find the range/ domain of a composite function. e.g fg(x) as it’s pretty common in function exam questions! Thank you
Good question! You consider the range of g(x), as these values become the input values for fg(x) i.e. it's domain. You then consider this function's range. Hope that makes sense!
hello sir, in part c of the final question i got a different inverse function, x-1/3. However it also gave me the right answer of -2.. i was wondering can there be more than 1 inverse function?
Hmm there can be different forms of the same inverse function, but they must be equivalent, and your function isn't equivalent to mine, so I think there must be an error there somewhere! (For example (1+x)/x is equivalent to 1/x + 1, so these could both be inverses for a different function, even though they look different!)
It will depend on the particular function - so the best advice is just to sub x=0 into the modulus function, and if the part inside the modulus lines is negative, just make it positive and keep working it out! That'll then certainly give you the y-intercept. Hope that makes sense :)
THANK YOU !!!! I HAVE MY MATHS MOCK ON MONDAY
Hope it goes well!
for part d on the second page, do u also hv to write x cant = 0
Jawad says thanks
HI Mr Bicen just wondering how would you work out the range of a composite function? (THANK YOU SO MUCH FOR YOUR VIDEOS!!)
You consider the range of g(x), as these values become the input values for fg(x) i.e. it's domain. You then consider this function's range. Hope that makes sense!
@ thank you, it does!!
Hi sir! Just wondering for the last question, if needed in an exam or just in general, what would be the easiest way to sketch these types of graphs? I always find it difficult to find the horizontal asymptotes in comparison to the vertical ones, sometimes there is also more than one horizontal asymptote and it just trips me up
These kinds of graphs are actually very hard to sketch, and in an exam situation, I wouldn't confidently sketch this without my graphics calculator - you should make sure you can sketch the standard reciprocal type (1/x type). But this one is definitely more complicated!
If you want to get better at graph sketching, there are probably some good TH-cam videos on it, but it is a very sophisticated topic that often comes up a lot in entrance exams for top universities!
Hi sir, I'm just wondering whether you'll be making videos like this for stats, mechanics and for further math. They've been a lot of help
Definitely for mech/stats, hopefully for FM too - time dependent.
@BicenMaths thank you so much sir they've been such a huge help for recapping chapters before tests.
does this cover all types of questions they can offer, or should I go through the playlist? Thanks a lot for these videos, they really help
It covers most, but definitely not all. It also doesn't really 'teach' all of these things, it is more designed to recap. So I would advise the playlist as your first approach, and then using these videos as a refresher! :)
Hi sir! I was wondering how do you find the range/ domain of a composite function. e.g fg(x) as it’s pretty common in function exam questions! Thank you
Good question! You consider the range of g(x), as these values become the input values for fg(x) i.e. it's domain. You then consider this function's range. Hope that makes sense!
Hi sir, sorry if I’m being a bit dumb but could you explain where the ‘-2’ came from? Thank you so much!
I'm sorry, I'm not sure which part of the video you are referring to! Any chance you could share a timestamp to help me?
hello sir, in part c of the final question i got a different inverse function, x-1/3. However it also gave me the right answer of -2.. i was wondering can there be more than 1 inverse function?
Hmm there can be different forms of the same inverse function, but they must be equivalent, and your function isn't equivalent to mine, so I think there must be an error there somewhere! (For example (1+x)/x is equivalent to 1/x + 1, so these could both be inverses for a different function, even though they look different!)
Sir if i have a modulus function and it has a y-intercept. Should i set x=0 for the negated or normal modulus to find that y intercept?
It will depend on the particular function - so the best advice is just to sub x=0 into the modulus function, and if the part inside the modulus lines is negative, just make it positive and keep working it out! That'll then certainly give you the y-intercept. Hope that makes sense :)