In mathematics, the domain or set of departure of a function is the set into which all of the input of the function is constrained to fall. It is the set X in the notation f: X ā Y, and is alternatively denoted as {\displaystyle \operatorname {dom} }.
Step-by-step explanation:
Formula
TheĀ domainĀ of a function is the set of all possible inputs for the function. For example, theĀ domainĀ of f(x)=xĀ² is all real numbers, and theĀ domainĀ of g(x)=1/x is all real numbers except for x=0. We can also define special functions whoseĀ domainsĀ are more limited.
Absolute value
As theĀ domainĀ ofĀ absolute valueĀ refers to the set of all possible inputĀ values, theĀ domainĀ of a graph consists of all the inputĀ valuesĀ shown on the x-axis. The range ofĀ absolute valueĀ is the set of possible outputĀ values, which are shown on the y-axis.
Notation
We can write theĀ domainĀ of f(x) in set builderĀ notationĀ as, {x | x ā„ 0}. If theĀ domainĀ of a function is all real numbers (i.e. there are no restrictions on x), you can simply state theĀ domainĀ as, 'all real numbers,' or use the symbol to represent all real numbers.
Rules
If a function contains a square root, set the equation inside the square root greater or equal to zero and solve. The resulting answer is theĀ domain. If a function contains a fraction, set the denominator not equal to zero and solve. The resulting answer is theĀ domain.
