Charismaztex
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Homework Statement
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 k(x)=\frac{x^2+4}{x+1}
(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
k(x)= g(x) +h(x), x belongs to (-a,a)
(iii) Explain why it is, or is not, true that k(x)=g(x) +h(x) for all x in the domain of k
Homework Equations
N/A
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