How do you determine if f(x) = x^3 - x^5f(x)=x3−x5 is an even or odd function?
1 Answer
Aug 19, 2016
f(x) is an odd function.
Explanation:
To determine if f(x) is even/odd, consider the following.
• If f(x) = f( -x) , then f(x) is even
AAx" in the domain"∀x in the domain Even functions have symmetry about the y-axis.
• If f( -x) = - f(x) , then f(x) is odd
AAx" in the domain"∀x in the domain Odd functions have half-turn symmetry about the origin.
Test for even
f(-x)=(-x)^3-(-x)^5=-x^3+x^5≠f(x)f(−x)=(−x)3−(−x)5=−x3+x5≠f(x) Since f(x) ≠ f( -x) , then f(x) is not even.
Test for odd
-f(x)=-(x^3-x^5)=-x^3+x^5=f(-x)−f(x)=−(x3−x5)=−x3+x5=f(−x) Since f( -x) = - f(x) , then f(x) is odd.
graph{x^3-x^5 [-10, 10, -5, 5]}
