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

1 Answer
Douglas K.
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 - 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

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