Real Functions

Pure Mathematics — Second Secondary

Finding the domain of a function

Type of function	Condition that determines the domain
Polynomial, such as 2x² − x + 1	The whole set of real numbers because any real number can be substituted
Rational, such as 1/(x − 4)	The denominator is not zero, so x ≠ 4
Square root, such as √(x + 1)	The expression under the root is greater than or equal to zero so x ≥ −1

When there is more than one condition, take the intersection of all of them.
Domains are written as intervals: the square bracket [ means the end value is included, the bracket ] means it is excluded, and ∞ and −∞ always take a round bracket.

Real Functions · 3 / 6