f(x)= x^3+2x^2+5 Can a function be both even or odd? Thnx!
R ryan_kidz Junior Member Joined Sep 11, 2005 Messages 89 Nov 29, 2005 #1 f(x)= x^3+2x^2+5 Can a function be both even or odd? Thnx!
stapel Super Moderator Staff member Joined Feb 4, 2004 Messages 16,582 Nov 29, 2005 #2 No more than a number can be both even and odd. But a function, like a non-whole number, can be neither even nor odd. Eliz.
No more than a number can be both even and odd. But a function, like a non-whole number, can be neither even nor odd. Eliz.
pka Elite Member Joined Jan 29, 2005 Messages 11,995 Nov 29, 2005 #3 This is truly trivial but: f(x)=0,⇒f(x)=f(−x),f(−x)=−f(x)\displaystyle f(x) = 0, \Rightarrow \quad f(x) = f( - x),\quad f( - x) = - f(x)f(x)=0,⇒f(x)=f(−x),f(−x)=−f(x).
This is truly trivial but: f(x)=0,⇒f(x)=f(−x),f(−x)=−f(x)\displaystyle f(x) = 0, \Rightarrow \quad f(x) = f( - x),\quad f( - x) = - f(x)f(x)=0,⇒f(x)=f(−x),f(−x)=−f(x).
