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#1 2005-11-03 02:56:58

Mathfun
Guest

Help Please With Functions!!

Let "a" and "b" be real numbers. We have 2 functions:

f(x) = ax + b|x|   and   g(x) = ax - b|x|

Show that if:  f(f(x)) = x    for every real x, then:

g(g(x)) = x   for every real x

Pleas help 'cause I haven't got any idea how to solve it.

#2 2005-11-03 04:17:25

mathfun
Guest

Re: Help Please With Functions!!

No one can help?? PLEASE It's veary important for me I have to present it tomorrow in class!!

#3 2005-11-03 04:46:59

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

Re: Help Please With Functions!!

And with that post, kylekatarn becomes a power member. Well done to you.

Back on topic, I tried it and got f(f(x)) = a (ax + b|x|) + b|(ax + b|x|)|.

For g(g(x)) to equal x when f(f(x)) is equal to x, then f(f(x) would have to be equal to g(g(x) and so b would have to be 0.

So now you have to prove that a (ax + b|x|) + b|(ax + b|x|)| ≠ x for all values of x when b ≠ 0. That's the tricky bit.


Why did the vector cross the road?
It wanted to be normal.

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#4 2005-11-03 10:02:15

MathsIsFun
Administrator
Registered: 2005-01-21
Posts: 7,711

Re: Help Please With Functions!!

Congrats kylekatarn, and thank you on behalf of everyone you have helped to get you there! (That was a curious sentence wasn't it?)


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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#5 2005-11-04 02:46:31

Mathfun
Guest

Re: Help Please With Functions!!

I still can't fix it..... ;(

#6 2005-11-05 10:56:21

Mathfun
Guest

Re: Help Please With Functions!!

Big BIg BIg BIg BIg thanks!!!!!!!!!

#7 2005-11-05 21:30:16

MathsIsFun
Administrator
Registered: 2005-01-21
Posts: 7,711

Re: Help Please With Functions!!

Most impressive, kylekatarn.


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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