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- February 18th 2011, 08:39 AM #1
## f(x) vs. f(-x) vs. -f(x)

Hello!

Could someone elaborate on what the difference is between f(x), f(-x), and -f(x)

Lets use the equation...

so if x=3 then f(x)=(5)(27)=135

and if x=-3 then f(x)=(5)(-27)=-135

what is -f(x) in this scenario? (when x=3)

is it simply or ?

- February 18th 2011, 08:49 AM #2

- February 18th 2011, 08:50 AM #3

- February 19th 2011, 04:28 AM #4

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For this particular function, because it involves only an odd power of x (and so is an "odd" function), f(-x) happens to be the same as -f(x). For example, f(-2)= 5(-2)(-2)(-2)= 5(4)(-2)= -40 while -f(2)= -(5)(2)(2)(2)= -5(4)(2)= -40.

However, if the function were , involving x only to an even power (and so an "even" function), we would have f(-x)= f(x). For example, f(-2)= 5(-2)(-2)= 20 which is equal to f(2)= 5(2)(2)= 20.

But most functions are neither "even" nor "odd". For example if f(x)= x+ 2, then f(-x)= -x+ 2 is not equal to either -f(x) nor f(x). For example, f(-2)= -2+ 2= 0 while f(2)= 2+ 2= 4.