How do you find the domain of an algebraic expression?

Question

For example:

2x - 5 or

x^2-2/x^2-4

Answer 1

if not previously given, the domain of an algebraic expression is taken to be the set of all real values of x for which f(x) is real and defined.

1) f(x) = 2x - 5

Domain:(-∞, ∞).

2) g(x) = (x^2 - 2) / (x^2 - 4)

is defined everywhere except at x = -2 and 2. so, the domain of g is

(-∞, -2) U (-2, 2) U ( 2, ∞) or

D = {x : x not equal to -2, 2 and x ε R }.