Question

How do you find the domain of `f(x) = sqrt(x^2 - 5x)`?

Answer 1

One finds the domain of a function that contains an even powered radical by asserting that the argument is greater than or equal to 0 and then solve the inequality.

Explanation:

We assert that `x^2 - 5x>=0`

Find the points were the function is 0:

`x^2 - 5x=0`

Factor:

`x(x - 5)=0`

`x = 0 and x = 5`

Because this function is that of a parabola that opens up, the function is negative between the roots, therefore, the domain is all of the values of x that are not between the roots:

`0 <= x and x >= 5`