Identifying functions from their equations

Question

Please explain in detail how to solve this problem.
thank you so much!

Identifying functions from their equations
Decide whether each relation defines y as a function of x. Give the domain:
y= 5/x-1

Answer 1

f : A →B is a function if for any element of set A there exists one and only one element of set B . Knowledge of domain and range and the strict compliance of the definition would separate functions from mere mathematical expressions.

A couple of examples: f: R→R with f(x)=x^{2 i} is a function; x² + y² = 1 is not a function. It boils down to the strict definition of a function! 

Answer 2

y = 5/(x - 1)

 

The domain is all real numbers x ≠ 1. 1 is excluded because this would cause division by zero, which is not possible.

 

For all other values of x, there is a unique value y which makes this a function.