(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

If f:(-a,a)-->Real numbers, then f can be rewritten as the sums of an even and an odd function

Let k: Real numbers\{-1}-->Real numbers be given by [tex]k(x)=\frac{x^2+4}{x+1}[/tex]

(i) Prove that there is no interval (-a,a) on which k is either even or odd

(ii) Find an even function g, an odd function h and a value a for which

[tex]k(x)= g(x) +h(x)[/tex], x belongs to (-a,a)

(iii) Explain why it is, or is not, true that [tex]k(x)=g(x) +h(x)[/tex] for all x in the domain of k

2. Relevant equations

N/A

3. The attempt at a solution

(i) Is it true that by proving k(x) does not equal k(-x) and k(x) does not equal -f(-x), we can prove that there is no interval (-a,a) on which k is either even or odd?

(ii) I am not quite sure here.

(iii) is it not true because x cannot be -1?

Thanks in advance,

Charismaztex

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Sums of even and odd functions

**Physics Forums | Science Articles, Homework Help, Discussion**