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Math Help - Functions!

  1. #1
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    Functions!

    If f(x) = (1-x)
    ------
    x
    what is f(f(x))

    please could you explain it too? I have no idea whatsoever what I'm doing.
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  2. #2
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    Quote Originally Posted by Anna-Banannna! View Post
    If f(x) = (1-x)
    ------
    x
    what is f(f(x))

    please could you explain it too? I have no idea whatsoever what I'm doing.
    here is how function notations work. whatever shows up in the brackets, you replace x with it (or whatever variable the function is defined for)

    example: if g(x) = x^2 + 2x + 3

    then, g(1) = (1)^2 + 2(1) + 3 = 6 ..........i replaced x with 1

    g(3) = (3)^2 + 2(3) + 3 = ..................i replaced x with 3

    g( ) = ( )^2 + 2( ) + 3 ...............i replaced x with ....(assume is in the domain of g(x) )


    what if we had another function?

    h(x) = x + 1

    then, g(h(x)) = (h(x))^2 + 2(h(x)) + 3 = (x + 1)^2 + 2(x + 1) + 3 ...........i replaced the x in g(x) with h(x)

    and

    h(g(x)) = (g(x)) + 1 = (x^2 + 2x + 3) + 1 = x^2 + 2x + 4 ............i replaced the x in h(x) with g(x)

    now, can you do your problem?
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  3. #3
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    thanks, I understand the ones you did, but all the divisions are confusing me. I have the top line as 1- (1-x/x) and my dad gave me the bottom line as 1-(x/x) but I don't get that bit either.

    Sorry, maths is NOT my best subject.
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Anna-Banannna! View Post
    thanks, I understand the ones you did, but all the divisions are confusing me. I have the top line as 1- (1-x/x) and my dad gave me the bottom line as 1-(x/x) but I don't get that bit either.

    Sorry, maths is NOT my best subject.
    the divisions don't matter. the same rule applies. wherever you see x in your function, replace it with f(x), then just write out what f(x) is, just as i did with my last two examples

    try again
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  5. #5
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    Um... 1- ((1-x)/x)/x)?
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  6. #6
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    Wait I get it!!!! Does 1= x/x?
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    Quote Originally Posted by Anna-Banannna! View Post
    Um... 1- ((1-x)/x)/x)?
    ok, i am not sure what you wrote. was the original function f(x) = \frac {1 - x}x?

    in that case, the first step would be: f(f(x)) = \frac {1 - (f(x))}{(f(x))}

    now what would it be?
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  8. #8
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    I did it!!! Whoo hoo I rock! Thanks for your help you've been brilliant!

    Luv ya loads Anna xxx
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    Quote Originally Posted by Anna-Banannna! View Post
    Wait I get it!!!! Does 1= x/x?
    yes, 1 = x/x

    but you don't have the right answer anyway, the thing you typed seems wrong--if i interpreted your question correctly
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  10. #10
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    Quote Originally Posted by Anna-Banannna! View Post
    I did it!!! Whoo hoo I rock! Thanks for your help you've been brilliant!

    Luv ya loads Anna xxx
    would you mind typing out your solution?
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