x̄ - > The domain of a mathematical expression

The domain of a mathematical expression refers to the set of all possible input values that can be substituted into the expression without causing an error or undefined result. The range of a mathematical expression refers to the set of all possible output values that the expression can produce.

For example, consider the function f(x) = x^2. The domain of this function is all real numbers, since any real number can be squared without causing an error. The range of the function is all non-negative real numbers, since the square of any real number is non-negative.

Another example is the function g(x) = 1/x. In this case, the domain of the function is all real numbers except for x = 0, since dividing by zero is undefined. The range of the function is also all real numbers except for 0, since any non-zero real number can be obtained by taking the reciprocal of another non-zero real number.

domain | f(x) = x/(x^2 - 1)

{x element R : x!=-1 and x!=1}

(assuming a function from reals to reals)

range | x^2 - x - 1

{y element R : y>=-5/4}

(assuming a function from reals to reals)

R (all real numbers)