Any fraction is not defined when its denominator is equal to 0. This is the key point that is used in finding the domain and range of a rational function.
Domain of Rational Function
The domain of a rational function is the set of all x-values that the function can take. To find the domain of a rational function y = f(x):
- Set the denominator ≠ 0 and solve it for x.
- Set of all real numbers other than the values of x mentioned in the last step is the domain.
Example: Find the domain of f(x) = (2x + 1) / (3x – 2).
Solution:
We set the denominator not equal to zero.
3x – 2 ≠ 0
x ≠ 2/3
Thus, the domain = {x ∈ R | x ≠ 2/3}