What is the domain of f(x)=sqrt((x-7)/(x+6)) ?

The domain of f(x)=sqrt((x-7)/(x+6)) is x = 7

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domain of f(x)=sqrt((x-7)/(x+6))

domain

f (x) = \frac{x - 7}{x + 6}

x < - 6 or x \geq 7

Interval Notation

(- \infty, - 6) \cup [7, \infty)

Solution steps

Find non-negative values for radicals:

x < - 6 or x \geq 7

Find undefined (singularity) points:

x = - 6

Combine real regions and undefined points for final function domain

x < - 6 or x \geq 7

What is the domain of f(x)=sqrt((x-7)/(x+6)) ?
The domain of f(x)=sqrt((x-7)/(x+6)) is x<-6\lor x>= 7