Results 1 to 5 of 5

Math Help - [SOLVED] Proving a function is one-to-one

  1. #1
    Junior Member
    Joined
    Apr 2009
    Posts
    70

    [SOLVED] Proving a function is one-to-one

    Hey guys,

    I am trying to prove the following function is one-to-one and onto.
    D=Q\{4}, R=\{2} and F-->R is f(x) = (2x + 3)/(x-4) for all x in D.

    Here is my work so far:

    One-to-One:
    Let f(x1) = f(x2)
    (2X1 + 3)/(X1 + 4) = (2X2 + 3)/(X2 + 4)
    Ok, so I know I have to end up with x1=x2, but from here, I get stuck. (seems more like an algebra problem from here, but can somebody show me how to end up with x1=x2 from here)

    Onto:
    Let y be an element of Q.
    Suppose f is onto.
    Then there exist some x in D s.t. f(x)=y.
    f(x) = (2x+3)/(x-4) = y
    Now I have to solve for x, and once again, I don't know how to solve for x. Seems I missed this part in Algebra class. Please show me how to solve for x.

    Also, am I on the right track to proving these
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,605
    Thanks
    1574
    Awards
    1
    Use simple notation: f(a)=f(b).
    \begin{gathered}<br />
  \frac{{2a + 3}}<br />
{{a - 4}} = \frac{{2b + 3}}<br />
{{b - 4}} \hfill \\<br />
  2ab - 8a + 3b - 12 = 2ab - 8b + 3a - 12 \hfill \\<br />
  11\left( {b - a} \right) = 0 \hfill \\<br />
  a = b \hfill \\ <br />
\end{gathered}
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Apr 2009
    Posts
    70
    Thanks, will work on that.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member
    Joined
    Apr 2009
    Posts
    70
    Ok, I was able to get the one-to-one part, x= (4y+3)/(y-2). However, now I am having a bit of trouble on the onto part. If I try to show that f((4y+3)/(y-2))= y ,plugging in for x in the original equation (f(x)=(2x+3)/(x-4)) and solving, I get 11/8 = y, but it needs to be just y, so that I can prove onto. Can anybody see where I am going wrong? Thanks
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Apr 2009
    Posts
    70
    Found my error: I was missing a (-) sign in there. Thanks for looking.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Proving equality - help please..
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: December 7th 2009, 05:18 AM
  2. [SOLVED] Proving
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: July 30th 2009, 08:27 AM
  3. [SOLVED] Proving?
    Posted in the Algebra Forum
    Replies: 2
    Last Post: June 5th 2009, 09:30 PM
  4. [SOLVED] proving bijectivity
    Posted in the Discrete Math Forum
    Replies: 3
    Last Post: April 11th 2009, 02:38 PM
  5. [SOLVED] Proving Combinations
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: March 25th 2009, 02:55 PM

Search Tags


/mathhelpforum @mathhelpforum