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Math Help - 2 discrete math prob

  1. #1
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    Nov 2006
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    2 discrete math prob

    i have two problems that i need help with real quick if someone could please help me...

    the first is..

    1. Let A=B=C=R, and let f:A-->B, g:B-->C be define by f(a)=a^2-3a+5 and g(b)=2b+4. Find:

    a) (f o g)(3)
    b) (g o f)(x)


    the second problem is:

    2. f(x)=4x-8. Find f^-1.


    Thanks for anyone that can help!!!!

    ~Rich
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  2. #2
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    Oct 2007
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    Central Coast, NSW
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    Quote Originally Posted by mathnoobie25 View Post
    i have two problems that i need help with real quick if someone could please help me...

    the first is..

    1. Let A=B=C=R, and let f:A-->B, g:B-->C be define by f(a)=a^2-3a+5 and g(b)=2b+4. Find:

    a) (f o g)(3)
    b) (g o f)(x)
    Ok, so for a) we have
    (f o g)(3) = f(g(3)) (function composition)
    = f(2*3 + 4) (by defn of g)
    = f(10) (simplifying)
    = 10^2 - 3*10 + 5 (by defn of f now)
    = 75.

    I'm sure you can do b) now - it's the same thing, just this time you won't end up with a number, you'll end up with something involving x's.


    Quote Originally Posted by mathnoobie25 View Post
    the second problem is:

    2. f(x)=4x-8. Find f^-1.


    Thanks for anyone that can help!!!!

    ~Rich
    Swap the f(x)'s and x's, like so:

    x = 4*f(x) - 8.

    Now we just solve for f(x) again, ie,

    f(x) = (x + 8)/4.

    You can check it's the inverse by evaluating f(f^-1(a)) and f^-1(f(a)). In both cases we want to end up with just a.

    Hope that helps.
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