C3 functions

http://www.examsolutions.net/a-level-maths-papers/Edexcel/Core-Maths/Core-Maths-C3/2007-June/paper.php#Q5

part b i can't get the value of the asymptote for the range of the original function

i've drawn the graph out and when x=0.5 y doesn't work but i don't know what to do from here onwards

Reply 1

B_9710

The asymptote is x=3. This gives 0 on denominator and of course division by 0 is not possible.

Reply 2

thegreatwhale

Original post by B_9710

The asymptote is x=3. This gives 0 on denominator and of course division by 0 is not possible.

so what can i do?

Reply 3

B_9710

Original post by thegreatwhale

so what can i do?

You said you couldn't find the asymptote. If it's part b you cannot do, it's just normal finding inverse, If you have a function y=f(x), just swap the x's and y's to find the equation of the inverse function. So for y=x+3, inverse has equation x=y+3, you can then rearrange if you want.

Reply 4

thegreatwhale

Original post by B_9710

ah sorry it was the domain of the inverse and range of the original which got me stuck

i got

y=\dfrac{e^x +1}{2}

Reply 5

B_9710

Well the domain of the inverse of g will be the range of the range of g as you said. It helps to know what the graph of y=g(x) looks like as it is quite a common function (rectangular hyperbola) and it has all range except 0, so

\nexists x \in \mathbb{R}, x\neq 3 : g(x)=0

Reply 6

thegreatwhale

Original post by B_9710

\nexists x \in \mathbb{R}, x\neq 3 : g(x)=0

but this is f(x) ????

Reply 7

B_9710

Original post by thegreatwhale

but this is f(x) ????

Oh I have misread your whole question. f is a simple transformation of the graph for ln x. You should probably be able to quickly recognise that it has all range.

Reply 8

thegreatwhale

Original post by B_9710

Oh I have misread your whole question. f is a simple transformation of the graph for ln x. You should probably be able to quickly recognise that it has all range.

ah, how would i know this? by looking at the inverse or some other method?

Reply 9

B_9710

Original post by thegreatwhale

ah, how would i know this? by looking at the inverse or some other method?

Well it's just a graph of lnx essentially. To get from lnx to the function f it is just 2 simple transformations so the graph will look more or less the same.
The graph of lnx is expected to be standard knowledge in C3. For y=lnx, there will be a vertical asymptote - y axis - and the range is

-\infty < y < \infty

Reply 10

thegreatwhale

Original post by B_9710

-\infty < y < \infty

ah yes ok so x can be any real number thanks

Reply 11

B_9710

Original post by thegreatwhale

ah yes ok so x can be any real number thanks

No, y can be any real number, x>0.
Although you could extend the domain to negative numbers (and complex numbers) if you wanted to, but for C3 purposes, x>0 for lnx.

Reply 12

thegreatwhale

Original post by B_9710

No, y can be any real number, x>0.
Although you could extend the domain to negative numbers (and complex numbers) if you wanted to, but for C3 purposes, x>0 for lnx.

ah thanks

all new stuff so learning more and more xd

Reply 13

B_9710

Original post by thegreatwhale

ah thanks

all new stuff so learning more and more xd

It's great that you're trying to learn it and get ahead. I would definitely recommend doing what you're doing. Get A* easy by exams next June.

Reply 14

thegreatwhale

Original post by B_9710

It's great that you're trying to learn it and get ahead. I would definitely recommend doing what you're doing. Get A* easy by exams next June.

Hopefully that's what i can do, haven't even learnt fp1 yet o.o which i need to do by the end of this summer but i'm thinking i need trig and c3 differentiation and c4 integration to do fp1....

Reply 15

JLegion

Original post by thegreatwhale

Hopefully that's what i can do, haven't even learnt fp1 yet o.o which i need to do by the end of this summer but i'm thinking i need trig and c3 differentiation and c4 integration to do fp1....

You don't

AS Maths differentiation is all you need. The implicit differentiation chapter of C4 may be handy, however, but is not required.
I can't recall any integration in FP1, but if I am wrong it will only be at a C2 level.