Basically the way I do these is by subbing in x=3, which gives (3+1)/(3-2) = 4/1 = 4, and then I sub in a really big number for example 500, which gives (500+1)/(500-2) = 1.006... From this you can see that as x tends towards infinity, f(x) tends towards 1. So the range is 1 < f(x) < 4

Would you be able to help with this question. 1 marker but I cant do what you explained here

https://www.youtube.com/watch?t=104&v=cdlij6HuwNI

Reply 1443

JamieF95

1

Original post by nayilgervinho

Where do I find these paper's?

http://www.madasmaths.com/archive_iygb_practice_papers_c3_practice_papers.html

Reply 1444

ACarter8

2

Can someone like that jan 2015 IAL paper pls :smile:

Reply 1445

BioAgent

10

Which solomon papers are the hardest for c3 in your opinion?

Reply 1446

Maths degree

11

anyone got any good tips for the domain and range questions ?

Reply 1447

adorablegirl1202

2

Original post by physicsmaths

I have noticed this year, M3 similar style to IAL, FP2 similar style to IAL not difficulty, physics today was also similar style to IAL.

Posted from TSR Mobile

was fp2 similar to ial?

Reply 1448

Gilo98

14

Original post by Maths degree

anyone got any good tips for the domain and range questions ?

a sketch, common sense and understanding of min and max values in fractions

Reply 1449

anonwinner

19

Original post by suyoof123

Would you be able to help with this question. 1 marker but I cant do what you explained here

https://www.youtube.com/watch?t=104&v=cdlij6HuwNI

Sure. For these questions I find the easiest way is to find the range of f(x), because the range of f(x) is the exact same as the domain of f^-1 (x) and vice versa.

f(x) = 1/(2x-1) , x > 1/2

Subbing x=1/2 into f(x) will not work because it will get f(x) = 1/0 which produces a 'math error'. So I would suggest subbing in a number slightly bigger than 1/2, for example you could do 0.5000001. If you sub that in you will find that you get a huge number, which suggests that f(x) has no upper limit, so now we need to find the lower limit. To do this, sub a really big number into f(x), for example 500. This will get f(x) = 1/(1000-1) = 0.001001... This suggests that the lower limit is 0.

So the range of f(x) is f(x) > 0 , which means the domain of f^-1 (x) is x>0

It is also useful to draw the graphs so you have an idea of the upper/lower limits

(edited 8 years ago)

Reply 1450

callyx27

4

So how's everyone feeling about tomorrow?

Reply 1451

TeeEm

19

Original post by sagar448

Yeah but was this a question from the C3 past paper? I want to know what question so I can have a go.

...
I wrote the ........ thing.

Original post by callyx27

So how's everyone feeling about tomorrow?

Worried haha, how about you?

Reply 1453

RonnieSaha

1

Original post by dnpnstn

Yeah that's right, you just need to give the values at the asymptote. Though if we get something like this in an exam e.g. cotx=1, you could be docked marks for writing tanx=infinity, you'd have to state that it tends towards infinity, and therefore tends towards 90/270 etc.

Thanks for the reply! I just find it weird that even though the curve never touches the points they are still solutions haha!

Reply 1454

suyoof123

2

Original post by anonwinner

Sure. For these questions I find the easiest way is to find the range of f(x), because the range of f(x) is the exact same as the domain of f^-1 (x) and vice versa.

f(x) = 1/(2x-1) , x > 1/2

Subbing x=1/2 into f(x) will not work because it will get f(x) = 1/0 which produces a 'math error'. So I would suggest subbing in a number slightly bigger than 1/2, for example you could do 0.5000001. If you sub that in you will find that you get a huge number, which suggests that f(x) has no upper limit, so now we need to find the lower limit. To do this, sub a really big number into f(x), for example 500. This will get f(x) = 1/(1000-1) = 0.001001... This suggests that the lower limit is 0.

So the range of f(x) is f(x) > 0 , which means the domain of f^-1 (x) is x>0

It is also useful to draw the graphs so you have an idea of the upper/lower limits

Thank you so much! twice you've helped, really appreciate it! and if they wanted the range of f'x, then you don't do anything as range of f'x is domain of f(x)

Also i would rather not draw the graphs for these, saves time and your method makes sense and is MUCH quicker.

Reply 1455

adorablegirl1202

2

june 2013 7b, not sure what to do

Reply 1456

anonwinner

19

Original post by suyoof123

Thank you so much! twice you've helped, really appreciate it! and if they wanted the range of f'x, then you don't do anything as range of f'x is domain of f(x)

Also i would rather not draw the graphs for these, saves time and your method makes sense and is MUCH quicker.

Yeh I rarely draw the graphs but everyone says you should so idk :P

Reply 1457

Gilo98

14

Can someone explain why the answer to June 2013 8b is 21/25 and not -21/25? If you see the equation as 21/25sec(x-73.74) then surely the min is negative??