What is the domain of f(x)=sqrt((x-4)/(2x-5)) ?

The domain of f(x)=sqrt((x-4)/(2x-5)) is x = 4

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domain of f(x)=sqrt((x-4)/(2x-5))

domain

f (x) = \frac{x - 4}{2 x - 5}

x < \frac{5}{2} or x \geq 4

Interval Notation

(- \infty, \frac{5}{2}) \cup [4, \infty)

Solution steps

Find non-negative values for radicals:

x < \frac{5}{2} or x \geq 4

Find undefined (singularity) points:

x = \frac{5}{2}

Combine real regions and undefined points for final function domain

x < \frac{5}{2} or x \geq 4

What is the domain of f(x)=sqrt((x-4)/(2x-5)) ?
The domain of f(x)=sqrt((x-4)/(2x-5)) is x< 5/2 \lor x>= 4