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

f (x) = 42.82819 x - 20.43748

f (x) = 5 csc (\frac{1}{2} π x + \frac{1}{6} π)

f (x) = x^{2} + 5 x + 4

x e^{x}

25 - x^{2}, - 5 \leq x < 5

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