Find the domain and range of the function `f(x) = |x-4|/(x-4)` 

Expert Answers
justaguide eNotes educator| Certified Educator

The range and domain of `f(x) = |x - 4|/(x - 4)` has to be determined.

The domain of a function is the set of values of x for which f(x) is defined. For f(x), when x = 4 the function takes the form `0/0 ` which is not defined. Therefore the domain is the set of real numbers except the number 4. The range of a function is the set in which f(x) lies if x lies in the domain. Here |x - 4| is either equal to (x - 4) or -(x - 4) depending on the sign of (x - 4). This gives the range as the set {-1, 1}

The domain of `f(x) = |x - 4|/(x - 4)` is R - {4} and the range is {-1, 1}