What is the domain of f(x)=sqrt((x^2-1)/(x^2+5x+6)) ?

The domain of f(x)=sqrt((x^2-1)/(x^2+5x+6)) is x = 1

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domain of f(x)=sqrt((x^2-1)/(x^2+5x+6))

domain

f (x) = \frac{x ^{2} - 1}{x ^{2} + 5 x + 6}

x < - 3 or - 2 < x \leq - 1 or x \geq 1

Interval Notation

(- \infty, - 3) \cup (- 2, - 1] \cup [1, \infty)

Solution steps

Find non-negative values for radicals:

x < - 3 or - 2 < x \leq - 1 or x \geq 1

Find undefined (singularity) points:

x = - 2, x = - 3

Combine real regions and undefined points for final function domain

x < - 3 or - 2 < x \leq - 1 or x \geq 1

f (x) = \frac{5 x ^{2} + 4}{x ^{2} + 3 x - 10}

f (x) = \frac{2}{x + 4}

f (x) = x^{2} - 1

\frac{e ^{x}}{7 + e ^{x}}

3 x^{2} - 5 x

What is the domain of f(x)=sqrt((x^2-1)/(x^2+5x+6)) ?
The domain of f(x)=sqrt((x^2-1)/(x^2+5x+6)) is x<-3\lor-2<x<=-1\lor x>= 1