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Math Help - Discrete math functions assignment

  1. #1
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    Discrete math functions assignment

    This is my last assignment for the discrete maths course. I am very swamped with work from other courses. Its due on Friday and don't know how to do the problems. Can someone recommend a good textbook to follow or website that migh help with discrete? The one we are using is DISCRETE MATHS by Goodaire and its not the best.

    Any help with the attached problems will be greatly appreciated. Thanks
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  2. #2
    MHF Contributor kalagota's Avatar
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    2) a) (-\infty, 4]
    b) [1, +\infty)

    3) what was your method??

    4)
    Let f:A \rightarrow B and g:B \rightarrow C be 1-1.. show that g \circ f is 1-1..

    let x,y \in A such that (g \circ f) (x) = (g \circ f) (y), i.e g(f(x)) = g(f(y))

    since g is 1-1, then f(x) = f(y).
    since f is 1-1, then x=y.
    therefore, g \circ f is 1-1. QED
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  3. #3
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    Quote Originally Posted by kalagota View Post
    2) a) (-\infty, 4]
    b) [1, +\infty)

    3) what was your method??

    4)
    Let f:A \rightarrow B and g:B \rightarrow C be 1-1.. show that g \circ f is 1-1..

    let x,y \in A such that (g \circ f) (x) = (g \circ f) (y), i.e g(f(x)) = g(f(y))

    since g is 1-1, then f(x) = f(y).
    since f is 1-1, then x=y.
    therefore, g \circ f is 1-1. QED
    Thank you. method for question 3 is by inspection same as question 2. Also could you explain to me how you got to your answers in question 2 and if you do 3 how you go about solving it too? Thanks
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  4. #4
    MHF Contributor kalagota's Avatar
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    for number 2 a)

    y= 4 - x^2

    you know that the range of y=x^2 is [0, +inf)...
    so, the range of y=-x^2 is (-inf, 0]..
    so if i add 4 to -x^2, the range would be (-inf, 4]

    computationally, this is it..

    0 \leq x^2 < \infty, so if i multiply -1 to all sides, the inequalities will change, i.e

    -(0) \geq -x^2 > -\infty or -\infty < -x^2 \leq 0

    if i add 4, the neg inf won't be affected since 4 is negligible with a very very "large" number negatively, therefore

    -\infty < 4 - x^2 \leq 4..

    just do the same thing with b)
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