What is the domain of f(x)=sqrt((x^2-5x+6)/(x^2-4)) ?

The domain of f(x)=sqrt((x^2-5x+6)/(x^2-4)) is x = 3

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domain of f(x)=sqrt((x^2-5x+6)/(x^2-4))

domain

f (x) = \frac{x ^{2} - 5 x + 6}{x ^{2} - 4}

x < - 2 or x \geq 3

Interval Notation

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

Solution steps

Find non-negative values for radicals:

x < - 2 or x \geq 3

Find undefined (singularity) points:

x = 2, x = - 2

Combine real regions and undefined points for final function domain

x < - 2 or x \geq 3

What is the domain of f(x)=sqrt((x^2-5x+6)/(x^2-4)) ?
The domain of f(x)=sqrt((x^2-5x+6)/(x^2-4)) is x<-2\lor x>= 3