What is the domain of f(x)=sqrt((x^2-25)/(x^2+4x+3)) ?

The domain of f(x)=sqrt((x^2-25)/(x^2+4x+3)) is x = 5

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domain of f(x)=sqrt((x^2-25)/(x^2+4x+3))

domain

f (x) = \frac{x ^{2} - 25}{x ^{2} + 4 x + 3}

x \leq - 5 or - 3 < x < - 1 or x \geq 5

Interval Notation

(- \infty, - 5] \cup (- 3, - 1) \cup [5, \infty)

Solution steps

Find non-negative values for radicals:

x \leq - 5 or - 3 < x < - 1 or x \geq 5

Find undefined (singularity) points:

x = - 1, x = - 3

Combine real regions and undefined points for final function domain

x \leq - 5 or - 3 < x < - 1 or x \geq 5

What is the domain of f(x)=sqrt((x^2-25)/(x^2+4x+3)) ?
The domain of f(x)=sqrt((x^2-25)/(x^2+4x+3)) is x<=-5\lor-3<x<-1\lor x>= 5