Does the formula: f(x) = 1/( x^2 – 2) define a function
f: R → R

A function f: Z → R

Question

Does the formula: f(x) = 1/( x^2 – 2) define a function  
f: R → R

A function f: Z → R

anonymous · Answer

it's a function as i think

anonymous · Answer

It is defined everywhere and there is no x in Z such that x^2=2

anonymous · Answer

The text is really weak in discussing the methods to solve. Should I just use arbitrary values to determine if the formula can be used for functions f: R to R and F; Z to R

anonymous · Answer

pretty much how i'd do it...^^^  same goes for $\large f:Z\rightarrow R $ ... it's easy to see that there is no integer such that when you square that integer, you will get 2....

anonymous · Answer

I am slightly confused on performing the steps to verify the results. Why would I need to get a 2 for the solution?

anonymous · Answer

is that last line a separate question?  or is it the same f as the one on the first?

anonymous · Answer

separate question

anonymous · Answer

I mean the f: Z to R applies to the question

anonymous · Answer

yeah, so in that second question, it's referring to the same function...

anonymous · Answer

yes

anonymous · Answer

I probably need to show my work on this. So how would I show this

anonymous · Answer

the function f maps the integers to the reals... $\large f:\mathbb{Z}\rightarrow\mathbb{R}  $