Real Analysis Answers

Find a bijection f:(a,b) --->(0,1)

prove that f(x) =x/(x squire+1),x is belongs to set of real number, is bijection.

S={n:n belongs to Z} what is the Sup S and Inf S? please explain the answer?

When a number set is not bounded above the supremum is plus infinity and when a set is not bounded below the infimum is minus infinity why?
please explain with examples

A number set has no supremum or it has a supremum which is infinity . does the two statement same ?

What is the domain of arcsin(Sin(x))?

For the functions
f(x) = x^2+1
g(x) = (e(x))/(x-1)

Calculate (f ∘ g)(x) & (g ∘ f)(x)
What are the Domains of (f ∘ g)(x) & (g ∘ f)(x)

If the co-domain does not contain all the elements of range , can it be a function?
like co-domain {3,4,5,6,7}
range {3,4 11}. normally we know range is a subset of co-domain. but here it does not . so is it possible?

what is the domain and range of sqrt of {(x-1)/(x+2)}

Test the following series for convergence:
a) ∑(n goes from 1 to infinity) n^(1/n).
b)∑(n goes from 1 to infinity) (((-1)^n)sin(3n x))/n^3