Lecture 1. Even / odd functions

Definition

• ƒ is even function: ƒ(-x)=ƒ(x)

• ƒ is odd if ƒ(-x)=-ƒ(x)

Examples

(a) ƒ(x)=√(,x2+1)*cos(x) is even because

ƒ(-x)=√(,(−x)2+1)*cos(−x)
=√(,x2+1)*cos(x)=ƒ(x)

(b) g(x)=√(3,x)+sin(x) is odd because

g*(−x)=√(3,−x)+sin(−x)
=−√(3,x)−sin(x)
=−(√(3,x)+sin(x))=−g(x)

(c) h(x)=ℇx√(,1+x3) is neither even or odd because

=ℇ(−x)√(,1−x3)≠h(x) or -h(x).