X+ (1/(x+5)^2) how do I show this is one to one and onto?

X+ (1/(x+5)^2) how do I show this is one to one and onto?

Answers
I'm afraid your question is unclear. Do you need to show that this expression is equivalent to something?
ianmoth
20 March 2012
Hi Jim. From my understanding of the question you're asking is this function a bijection (one to one and onto). You've got an X and x in the expression, are they supposed to be the same? if they are then unfortunately this is not one to one (injective), but is onto (surjective). I'm assuming that you want this to be f(x)=x+(1/(x+5)^2). To see if it's one to one you need to make sure that for every value of f(x) there is a unique value of x. ie for f(x)=x+2 if f(x)=5 then x=3. However f(x)=x^2, if f(x) =4 the x=2,-2 i.e not unique. So you can either prove that it's not unique by finding 2 values of x which come up with the same f(x) or prove that it is unique by showing that for each f(x), x can be expressed uniquely. That's a lot of information to take in in one go, let me know if you need any more help with the understanding.
sinsua
21 March 2012
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