How do you determine if #f(x) = x^3 + x# is an even or odd function?
2 Answers
It is an odd function since
Explanation:
A function
So in this case hence it is odd.
For example, select
Then
Note also that all odd functions which are piecewise continuous and differentiable and having period
odd function
Explanation:
To determine if a function is even/odd the following applies.
• If f(x) = f( -x) then f(x) is even ,
# AAx # Even functions have symmetry about the t-axis.
• If f(-x) = - f(x) then f(x) is odd ,
#AAx# Odd functions have symmetry about the origin.
Test for even :
f( -x) =
#(-x)^3 + (-x) = - x^3 - x ≠ f(x)# , hence not evenTest for odd :
#- f(x) = - (x^3 + x) = - x^3 - x =f(-x) # , hence function is odd.Here is the graph of f(x). Note symmetry about O.
graph{x^3+x [-10, 10, -5, 5]}
