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

1 Answer
Oct 8, 2017

Answer:

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#