What is the domain of f(x)= 1/(x^2-4x)?

1 Answer
Oct 15, 2017

All real numbers except x=0 and x=4

Explanation:

The domain of a function is simply the set of all x-values that will output real y-values. In this equation, not all x-values will work as we cannot divide by 0. Thus, we need to find when the denominator will be 0.

x^2-4x=0

x*(x-4)=0

Using the Zero Property of Multiplication, if x=0 or x-4=0, then x^2-4x=0 will be 0.

Thus, x=0 and x=4 should not be part of the domain as they would result in a non-existent y-value.

This means the domain is all real numbers except x=0 and x=4.

In set notation, this can be written as x in RR " such that " x!=0 and x!=4