anonymous
  • anonymous
each function is either even or odd .use f(-x) to state which situation applies f(x)=5x^3-8x please help
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
do you get the difference between even and odd functions?
anonymous
  • anonymous
This is a good resource to start with: http://www.purplemath.com/modules/fcnnot3.htm Feel free to ask if you still have any questions
UnkleRhaukus
  • UnkleRhaukus
Find f(-x) :

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anonymous
  • anonymous
i will look at it thank you
UnkleRhaukus
  • UnkleRhaukus
\[f(x)=5x^3-8x\] so \[f(-x)=5(-x)^3-8(-x)\] .. can you simplify this?
anonymous
  • anonymous
-5x^3+8x
UnkleRhaukus
  • UnkleRhaukus
good, so you found \[f(-x)=-5x^3+8x\] if we now factor out the negative sign\[f(-x)=-(5x^3-8x)\] We have the negative of the original function\[f(-x)=-f(x)\] This is the definition of an odd function.
anonymous
  • anonymous
thank you :)
UnkleRhaukus
  • UnkleRhaukus
if we had gotten\[f(-x) = f(x)\], (after simplification), it would have been an even function

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