When exchanging mail, e-mail or posting information anywhere on the web with the cosine clan, we also need another form of identification in order for us not to be deceived by our many enemies. -When we send mail or post information on the internet, we include the equation of a function that is even.
-The cosine clan, on the other hand, includes the equation of a function that is odd.
Of course, all of this is done subtly using a colour not normally visible to the human eye.
To throw off our enemies even more, so they don't catch onto us, we also add an equation that is neither even or odd. For this equation, we use visible ink.
These letter rules, however, exclude this post because only our students who have completed stage one of the training would be able to reach this.
Are the following equations from the sine clan, the cosine clan, or from our enemies? (Don't Worry, we did not use invisible ink for the equation)
If a function is even, that means f(x) must equal f(-x). Therefore, let us start by replacing all the "x" values with "-x."
A negative number multiplied by itself an even number of times makes the end result a positive number. Therefore, the equation is left virtually unchanged.
Since f(x) = f(-x), the function is even. Since the function is even, this equation was written by the sine clan.
A Function is considered odd if -f(x) = f(-x). Therefore, to get -f(x), we multiply the whole equation by -1.
Now we need to get the value of f(-x). Once again, to do this we replace all of the "x" values with "-x."
When you multiply 2 negative numbers, the product of those two number will be positive.
Therefore, since -f(x) = f(-x), the function is considered odd, meaning this equation would belong to the cosine clan.
Last One
First we check if it's even b replacing all "x" values with "-x."
Since f(x) =/= f(-x) the function is not even. Therefore we need to check if the function is odd, by multiplying the whole equation by -1.
Since -f(x) =/= f(-x), the function is neither even or odd. Therefore, we can assume that something with an equation like this was probably posted up by the enemy
Well...if you have finished reading through this letter, please continue onto the next site by clicking HERE!
Or you can copy and paste the following link into your web browser:
http://ia301543.us.archive.org/1/items/Mathemaninja-Q3_307/mathcaf.swf
