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    http://www.examsolutions.net/a-level...e/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
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    The asymptote is x=3. This gives 0 on denominator and of course division by 0 is not possible.
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    (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?
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    (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.
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    (Original post by B_9710)
    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.
    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}
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    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 .
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    (Original post by 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 .
    but this is f(x) ????
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    (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.
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    (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?
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    (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 .
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    (Original post by B_9710)
    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 .
    ah yes ok so x can be any real number thanks
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    (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.
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    (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
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    (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.
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    (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....
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    (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.
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    (Original post by JLegion)
    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.
    sounds good... so i guess i can move onto it right away....
 
 
 
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