What is the domain of f(x)=sqrt((x(x+7))/(x^2+5x+6)) ?

The domain of f(x)=sqrt((x(x+7))/(x^2+5x+6)) is x = 0

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domain of f(x)=sqrt((x(x+7))/(x^2+5x+6))

domain

x \leq - 7 or - 3 < x < - 2 or x \geq 0

Interval Notation

(- \infty, - 7] \cup (- 3, - 2) \cup [0, \infty)

Solution steps

Find non-negative values for radicals:

x \leq - 7 or - 3 < x < - 2 or x \geq 0

Find undefined (singularity) points:

x = - 2, x = - 3

Combine real regions and undefined points for final function domain

x \leq - 7 or - 3 < x < - 2 or x \geq 0

What is the domain of f(x)=sqrt((x(x+7))/(x^2+5x+6)) ?
The domain of f(x)=sqrt((x(x+7))/(x^2+5x+6)) is x<=-7\lor-3<x<-2\lor x>= 0