Find the Domain of Rational Functions

A step by step tutorial, with detailed solutions, on how to find the domain of rational functions is presented. Problems matched to the exercises with solutions at the bottom of the page are also presented.

Definition of the Domain of a Function

For a function f defined by an expression with variable x, the implied domain of f is the set of all real numbers variable x can take such that the expression defining the function is real. The domain can also be given explicitly.

also Step by Step Calculator to Find Domain of a Function




Example 1: Find the domain of function f defined by

rational function example 1

Solution to Example 1

Matched Problem 1: Find the domain of function f defined by

rational function  - matched problem 1




Example 2: Find the domain of function f defined by

rational function example 2

Solution to Example 2

Matched Problem 2: Find the domain of function f defined by:

rational function matched 2



Example 3: Find the domain of function f defined by:

rational function example 3

Solution to Example 3

Matched Problem 3: Find the domain of function f defined by:

rational function matched 3



Example 4: Find the domain of function f defined by:

rational function example 4

Solution to Example 4

Matched Problem 4: Find the domain of function f defined by:

rational function matched 4



Example 5: Find the domain of function f defined by:

rational function example 5

Solution to Example 5

Matched Problem 5: Find the domain of function f defined by:

rational function matched 5



Answers to matched problems
  1. (-∞ , 6) ∪ (6 , + ∞)
  2. (-∞ , + ∞)
  3. (-∞ , - 4 / 3) ∪ (- 4 / 3 , 2) ∪ (2 , ∞)
  4. (-∞ , - 4) ∪ (- 4 , 3 / 7) ∪ (3 / 7 , ∞)
  5. (-∞ , -3) ∪ (-3 , 0) ∪ (0 , 1) ∪ (1 , ∞)



More Find domain and range of functions, Find the range of functions, find the domain of a function and mathematics tutorials and problems.