For the function f defined by f(x)=x^2+2x+3 find f(−x),−f(x) , and −f(−x).

Hello from MrBillDoesMath!

See discussion below

Discussion:

A real brain teaser!

If f(x) = x^2 + 2x + 3, then

a. f(-x) = (-x)^2 + 2(-x) +3

         =  x^2    -2x      + 3

b. - f(x) = - (x^2 + 2x + 3)  = -x^2 -2x - 3

c. Using a) above

   -f(-x) = - (x^2 -2x + 3 ) = -x^2 + 2x - 3

Note that f(x) is not an even function ( f(x) = f(-x) ) or an odd function ( f(-x) = - f(x))

Thank you,

MrB