Question

Find an even and odd function whose sum or difference = (x+1)/(x-1).
How do I approach this question?

Answer 1

Say f is the even function you're looking for, and g is the odd function.
f(-x) = f(x) and g(-x) = -g(x)
You have that :
\[f(x)+g(x) = \frac{ x+1 }{ x-1 }\] Also: \[f(-x)+g(-x) = \frac{ -x+1 }{ -x-1 }\] Which is equivalent to : \[f(x)-g(x) = \frac{ x-1 }{ x+1 }\] Now all you have to do is solve this system to find f and g.

Answer 2

Thank you!

Answer 3

Welcome !