I have trouble with this questions

f:[3,infinity)-->R f(x)=x^2 -6x +10

The answer for this (in mcqs) is

f^-1:[1,infi)-->[3,infi), f^-1(y)= 3+ (y-1)^-.5

I do know how to get the f inverse but i do not know how to get the domains and ranges.

Can you explain what is meant from [1,infi)-->[3,infi) ?

2nd question

f(x)={x x is rational

-x x is irrational

g(x)={sinx x is rational

x^3 x is irrational

Can you comment on the existance of limx->0f(x) and lim->0g(x)

Thank you

PS. sorry about the written format. I don't know how to use maths sybols(is there a link which tells how)