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

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

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

domain

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

x \leq 0 or x > 4

Interval Notation

(- \infty, 0] \cup (4, \infty)

Solution steps

Find non-negative values for radicals:

x \leq 0 or x > 4

Find undefined (singularity) points:

x = 4

Combine real regions and undefined points for final function domain

x \leq 0 or x > 4

f (x) = x^{2} - 6 x - 7 + 5 - 2 x

f (x) = \frac{( 3 - 4 ) ^{2}}{3 - 3}

+ 7 c - 14

p (x) = \frac{1}{2} e^{x}

f (x) = x^{2} - 4 + \frac{1}{x ^{2} - 9} + x

What is the domain of f(x)=sqrt(x/(x-4)) ?
The domain of f(x)=sqrt(x/(x-4)) is x<= 0\lor x>4