1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

New guy needs help

  1. Aug 20, 2005 #1


    User Avatar

    Hello everyone.
    I am Jeremy and I hail from Trinidad. I am in my mid thirtys and currently a network administrator for a shipping firm (import/exports).

    After passing through one hell of a divorce I decided to pursue my degree in Physics. I was a math geek back in seconday school and had a knack for Physics so getting this degree should prove to rekindle an old flame.

    The first step in this long journey is to get 3 A levels (University of Cambridge Advance Levels). The three A levels I have to get are as follows: Mathematics, Physics and Futher Mathematics. I am now self studying the first two.

    I need your help to enable me achieve my goal. I can do most of the work myself but there are some things that escape my understanding. Thus, whatever input you guys can give me is well appreciated.

    (This is an A level question; I did not know weather I should have placed this post in the College section or if A levels and grade 12 are at the same skill level- please forgive me if I posted this in the wrong place)

    Here is a problem that I couldn't figure out:

    Provided that x is real, prove that the function [2(3x+1)]/[3(A-9)]
    can take all real values. (A = x squared)

    Again, thank you for your help and support.


    Oh yeah I have 10 gmail invites to give away. Just ask and I will email it to you.
    Last edited: Aug 20, 2005
  2. jcsd
  3. Aug 20, 2005 #2


    User Avatar
    Science Advisor
    Homework Helper

    Can you factor


  4. Aug 20, 2005 #3
    Just make a sign chart of each term of this function and multiply the signs. beware that x =3 and -3 will yield infinities

  5. Aug 20, 2005 #4


    User Avatar

    I can factorize the difference of 2 squares.

    What is a sign chart?
  6. Aug 20, 2005 #5
    I am sure you know this...

    suppose you have y = 2x - 2

    for x = 1, y = 0

    Since the slope 2 is positive this function rises as x rises so this implies

    1) x < 1 => y < 0

    2)x > 1 => y > 0

    That is a sign chart...Just do this for each term after having factorized the x² term

  7. Aug 20, 2005 #6


    User Avatar
    Gold Member

    You can show that this function takes on any value by showing that there exists some value of x that results in each value of of the function(call it y). This can be done by finding the inverse function:
    [tex]y = \frac{2(3x+1)}{3(x^2 - 9)}[/tex]
    [tex]3yx^2-27y = 6x+3[/tex]
    [tex]3yx^2 - 6x -27y -3 = 0[/tex]
    and by the quadratic formula:
    [tex]x = \frac{6 +/- \sqrt{36 + 322y^2 +36y}}{6y}[/tex]
    This inverse function(s) is defined for all real values of y, except 0, so there must be at least one value of x that yields every real value of y, except, possibly, 0. However, x=-1/3 gives 0 for the function, so that completes all real values.

    By the way, if you want to know how to write equations, look at this https://www.physicsforums.com/showthread.php?t=8997
  8. Aug 20, 2005 #7


    User Avatar

    the satisfaction that one gets when he finally knows the solution to a complex problem.

    Thanks Leon
    Last edited: Aug 20, 2005
  9. Aug 21, 2005 #8


    User Avatar
    Staff Emeritus
    Science Advisor

    The satisfaction of having solved it yourself is even greater!
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: New guy needs help