What is the domain of f(x)=sqrt((-x)/(8-x)) ?

The domain of f(x)=sqrt((-x)/(8-x)) is x 8

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domain of f(x)=sqrt((-x)/(8-x))

domain

f (x) = \frac{- x}{8 - x}

x \leq 0 or x > 8

Interval Notation

(- \infty, 0] \cup (8, \infty)

Solution steps

Find non-negative values for radicals:

x \leq 0 or x > 8

Find undefined (singularity) points:

x = 8

Combine real regions and undefined points for final function domain

x \leq 0 or x > 8

What is the domain of f(x)=sqrt((-x)/(8-x)) ?
The domain of f(x)=sqrt((-x)/(8-x)) is x<= 0\lor x>8