If $$f(x) = {{\sqrt {x - 1} } \over {x - 4}}$$, defines a function on R, then what is its domain?

When one of the following is correct in respect of the function f : R $$\to$$ R⁺ defined as f(x) = |x + 1| ?

Suppose f : R $$\to$$ R is defined by $$f(x) = {{{x^2}} \over {1 + {x^2}}}$$. What is the range of the function?

For f to be a function, what is the domain of f, if $$f(x) = {1 \over {\sqrt {|x| - x} }}$$ ?