Question

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

Answer 1

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`