Functions, even, odd or neither?

Algebra
Tutor: None Selected Time limit: 1 Day

Can I get help with 11, 13, 14 and 15?

Sep 24th, 2015

Thank you for the opportunity to help you with your question!

11) if  h(x) is even then h(-x) = h(x) 

if g(x) is odd, then g(-x) = -g(x)

f(x) = g(x)*h(x)

f(-x) = g(-x) * h(-x)

f(-x) = -g(x) * h(x) (based on above)

f(-x) = -f(x).  Thus, odd


13) Let g(x) and h(x) be arbitrary odd functions

this means that g(-x) = -g(x) and h(-x) = -h(x)


Let f(x) = g(x) + h(x) 

f(-x) = g(-x)  + h(-x)

f(-x) = -g(x) - h(x)

f(-x) = -(g(x) + h(x))

f(-x) = -f(x)

QED


14)There are plenty of functions that are not even or odd. For example, consider a function that is the sum of an even and odd function. It is neither odd nor even. 


15) Even means that it is reflective over y-axis. Odd means it is reflective over origin. 

Please let me know if you need any clarification. I'm always happy to answer your questions.
Sep 24th, 2015

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