Assume p is an even function and q is an odd function, given p,q lies on the entire real line, determine if p @ q is an even or odd function

Winston Todd

Winston Todd

Answered question

2022-10-27

Assume p is an even function and q is an odd function, given p,q lies on the entire real line, determine if p q is an even or odd function
Fundamentally,
Even function: f ( x ) = f ( x )
Odd function: f ( x ) = f ( x )
can I say that p q is an odd function because:
( p q ) ( x ) = p ( q ( x ) ) = p ( q ( x ) ) = ( p q ) ( x ) ?

Answer & Explanation

t5an1izqp

t5an1izqp

Beginner2022-10-28Added 13 answers

Both compositions are even:
p ( q ( x ) ) = p ( q ( x ) ) = p ( q ( x ) ) , and q ( p ( x ) ) = q ( p ( x ) ) .

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