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    Hi I am really confused on how to work out part c in question 3. I have spent ages working it out and can't get it right. Thanks for any help.
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    (Original post by Meggy moo 1)
    Hi I am really confused on how to work out part c in question 3. I have spent ages working it out and can't get it right. Thanks for any help.
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    To find the equation of f(x+1) simply replace all references to "x" in f(x) with "x+1".
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    (Original post by 16Characters....)
    To find the equation of f(x+1) simply replace all references to "x" in f(x) with "x+1".
    Thank you, I've done that. But I don't understand how/if I need to expand out that substitution? Because I just get left with (x + 1)^2 - (x + 1)^3
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    (Original post by Meggy moo 1)
    Thank you, I've done that. But I don't understand how/if I need to expand out that substitution?
    What do you have exactly at the moment?
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    (Original post by 16Characters....)
    What do you have exactly at the moment?
    Sorry I just edited my last message to show what I got but I get (x + 1)^2 - (x + 1)^3 when I expand it out
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    (Original post by Meggy moo 1)
    Sorry I just edited my last message to show what I got but I get (x + 1)^2 - (x + 1)^3 when I expand it out
    Yeah, just sub in x=0
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    (Original post by Meggy moo 1)
    Sorry I just edited my last message to show what I got but I get (x + 1)^2 - (x + 1)^3 when I expand it out
    I would keep it factorised to be honest, looks neater but it really does not matter. All the question now wants is for you to find the y-intercept so there is no particular best way to write your answer.
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    for part c, when subbing in x+1, you should just have (x+1)^2*(1-(x+1)) which simplifies to (x+1)^2 * (-x) i.e.y= -x(x+1)^2there is no need to expand anything ... the answer is directly visible ... but if not, just sub x=0 in ..
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    (Original post by 16Characters....)
    I would keep it factorised to be honest, looks neater but it really does not matter. All the question now wants is for you to find the y-intercept so there is no particular best way to write your answer.
    What confuses me is how to work out the equation as the answer in the back of the book is -x(x + 1)^2
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    (Original post by dpm)
    for part c, when subbing in x+1, you should just have (x+1)^2*(1-(x+1)) which simplifies to (x+1)^2 * (-x) i.e.y= -x(x+1)^2there is no need to expand anything ... the answer is directly visible ... but if not, just sub x=0 in ..
    Will you need to expand the brackets to work out that it simplifies to that as I don't see how you've got that
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    (Original post by Meggy moo 1)
    Will you need to expand the brackets to work out that it simplifies to that as I don't see how you've got that
     f(x) = x^2 (1-x)

     f(x+1) = (x+1)^2(1-(x+1))

    Simplify this, you should get what they want you to get. No expanding needed.


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    (Original post by kingaaran)
     f(x) = x^2 (1-x)

     f(x+1) = (x+1)^2(1-(x+1))

    Simplify this, you should get what they want you to get. No expanding needed.


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    Now I feel really silly because I can't even do that because I don't see how you can simplify without expanding


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    (Original post by Meggy moo 1)
    Now I feel really silly because I can't even do that because I don't see how you can simplify without expanding


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    What is 1-(x+1)?


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    (Original post by kingaaran)
    What is 1-(x+1)?


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    -x ?


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    (Original post by Meggy moo 1)
    -x ?


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    Hence,  f(x+1) = (x+1)^2 (1-(x+1)) = (x+1)^2(-x) = -x(x+1)^2

    That is what the book wanted right?


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    (Original post by Meggy moo 1)
    -x ?


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    yes
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    (Original post by kingaaran)
    Hence,  f(x+1) = (x+1)^2 (1-(x+1)) = (x+2)^2(-x) = -x(x+1)^2

    That is what the book wanted right?


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    Yeah! Thank you so much! I felt really silly then 😄


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    (Original post by dpm)
    yes
    Thank you, I understand now


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    (Original post by Meggy moo 1)
    Thank you, I've done that. But I don't understand how/if I need to expand out that substitution? Because I just get left with (x + 1)^2 - (x + 1)^3
    Yeah just sub into original equation(s)
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    (Original post by AlphaArgonian)
    Yeah just sub into original equation(s)
    Oh okay yeah that makes sense now, thank you


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