How do you determine if f(x)=2x5−3x2+2 is an even or odd function?
1 Answer
Mar 28, 2016
Neither
Explanation:
To determine if a function is even/odd the following applies.
• If f(x) = f( -x) then f(x) is even ,
∀x Even functions have symmetry about the y-axis.
• If f( -x) = - f(x) then f(x) is odd ,
∀x Odd functions have symmetry about the origin.
---------------------------------------------------------------- Test for even :
f( -x)
=2(−x)5−3(−x)2+2=−2x5−3x2+2 since f(x) ≠ f( -x) , then f(x) is not even.
----------------------------------------------------------- Test for odd :
−f(x)=−(2x5−3x2+2)=−2x5+3x2−2 since -f(x) ≠ f( -x) , then f(x) is not odd.
