Domain:
Some general rules to be followed while determining the domain of a function:
1. The denominator of a function must be non-zero.
2. For even-indexed roots (e.g., √x), the argument must be non-negative.
3. The argument of a logarithm must be strictly positive. The base of logarithm must be positive but not 1.
Range:
1. Replace f(x) with y.
2. Solve the equation for x.
3. Analyze the new expression for any restrictions on y (similar like domain).
Example: For y = 1 / x, solving for x gives x = 1 / y. Since y is in the denominator, y cannot be 0. Therefore, the Range is (−∞ 0) U,(0, ∞).
