Finding the domain of a function from its rule is not difficult. Look at the examples below carefully.
1) Give the domain of each.
a) f(x) = 3/(x - 5) The domain consists of all numbers for x that are defined for the function. Since the function doesn't exist at x = 5 ( it makes the denominator 0), the domain is all real numbers but 5.
b) f(x) = Since 4 - x is under the radical, 4 - x must be greater than or equal to zero, otherwise the answers will be imaginary. To find the domain, solve the inequality 4 - x > 0.
-x > -4
x < 4. Thus, all numbers less than or equal to 4 represent the domain for this function.