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

Oct 8, 2017

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 ${x}^{2} - 5 x \ge 0$

Find the points were the function is 0:

${x}^{2} - 5 x = 0$

Factor:

$x \left(x - 5\right) = 0$

$x = 0 \mathmr{and} x = 5$

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:

$0 \le x \mathmr{and} x \ge 5$