New guy needs help

  • Thread starter Tau
  • Start date
  • #1
Tau
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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.

Jeremy

Oh yeah I have 10 gmail invites to give away. Just ask and I will email it to you.
 
Last edited:

Answers and Replies

  • #2
Tide
Science Advisor
Homework Helper
3,076
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Can you factor

[tex]x^2-9[/tex]

?
 
  • #3
3,763
9
Just make a sign chart of each term of this function and multiply the signs. beware that x =3 and -3 will yield infinities

marlon
 
  • #4
Tau
14
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I can factorize the difference of 2 squares.

What is a sign chart?
 
  • #5
3,763
9
Tau said:
What is a sign chart?
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

marlon
 
  • #6
LeonhardEuler
Gold Member
859
1
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
 
  • #7
Tau
14
0
Ahhhhhhhhhhhhhhhhh
the satisfaction that one gets when he finally knows the solution to a complex problem.

Thanks Leon
 
Last edited:
  • #8
HallsofIvy
Science Advisor
Homework Helper
41,833
956
The satisfaction of having solved it yourself is even greater!
 

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