What is the domain of f(x)=(sqrt(2x-5))/(x^2-6x) ?

The domain of f(x)=(sqrt(2x-5))/(x^2-6x) is 5/2 6

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domain of f(x)=(sqrt(2x-5))/(x^2-6x)

domain

\frac{5}{2} \leq x < 6 or x > 6

Interval Notation

[\frac{5}{2}, 6) \cup (6, \infty)

Solution steps

Find non-negative values for radicals:

x \geq \frac{5}{2}

Find undefined (singularity) points:

x = 6, x = 0

Combine real regions and undefined points for final function domain

\frac{5}{2} \leq x < 6 or x > 6

What is the domain of f(x)=(sqrt(2x-5))/(x^2-6x) ?
The domain of f(x)=(sqrt(2x-5))/(x^2-6x) is 5/2 <= x<6\lor x>6