Math Is Fun Forum

g(x)=x[sup]2[/sup]-1
is defined for all R-->R

To show that g(x) is not one-one we need to show that g(x[sub]1[/sub]) = g(x[sub]2[/sub]) for some x[sub]1[/sub] ≠ x[sub]2[/sub]

Let g(x[sub]1[/sub]) = g(x[sub]2[/sub])

x[sub]1[/sub][sup]2[/sup] - 1 = x[sub]2[/sub][sup]2[/sup] - 1

x[sub]1[/sub][sup]2[/sup] = x[sub]2[/sub][sup]2[/sup]

x[sub]1[/sub][sup]2[/sup] - x[sub]2[/sub][sup]2[/sup] = 0

(x[sub]1[/sub] - x[sub]2[/sub])(x[sub]1[/sub] + x[sub]2[/sub]) = 0

x[sub]1[/sub] - x[sub]2[/sub] = 0 or x[sub]1[/sub] + x[sub]2[/sub] = 0

x[sub]1[/sub] = x[sub]2[/sub] or x[sub]1[/sub] = - x[sub]2[/sub]

i. e. x[sub]1[/sub] = x[sub]2[/sub] or x[sub]1[/sub] ≠ x[sub]2[/sub]

However.. this may not be the only proof.

agreed!

ok.. tell me..
is "the rule" pre-defined?

or you can/will change it at times?

how and when does "the rule change"?

its just below

i can see the contents if i click on "edit" but its STILL NOT VISIBLE ! 

hi mod

i wanted to delete the "repeated" or "misplaced" posts...
like... earlier i posted this same issue in same thread where i had the problem.
but then i wanted to delete that post (coz i have it now posted in "Suggestions and Comments") which i had to achieve by closing Opera and opening Chrome?

which OS do you use?

it's XP-Professional 2002 SP-2 here in our institute!

Hi phrontister!
sorry i just couldn't resist myself from posting 5239 again!

u'r missing a word between SHOT and SHED
i'm not very good at this game 

hi gurthbruins!

i hope you might find the exact solution for me!

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Definition of Prime number: A number which has EXACTLY TWO factors (divisors) is called a Prime number!
e. g. 2 has factors 1, 2 (exactly two factors) hence is a Prime number.
3 has factors 1, 3 (exactly two factors) hence is a Prime number.
4 has factors 1, 2, 4 (more than two factors) hence is Not Prime. Such numbers are called Composite numbers.
13 has factors 1, 13 (exactly two factors) hence is a Prime number.

Note: We consider the positive natural number divisiors only.

Here are a few basic observations (proofs to be given later):

> 1 is neither prime nor composite. It has EXACTLY ONE factor.

> All prime numbers, except 2, are odd numbers.

> No other prime number ends in a (has its unit's place) 2 or 5  !

> The minimum difference possible between any two prime numbers is 2.
2 and 3 are the only exceptions which have a difference of 1.