What is the domain of f(x)=sqrt((x^2-1)/(x^2-3)) ?

The domain of f(x)=sqrt((x^2-1)/(x^2-3)) is x sqrt(3)

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domain of f(x)=sqrt((x^2-1)/(x^2-3))

domain

f (x) = \frac{x ^{2} - 1}{x ^{2} - 3}

x < - 3 or - 1 \leq x \leq 1 or x > 3

Interval Notation

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

Solution steps

Find non-negative values for radicals:

x < - 3 or - 1 \leq x \leq 1 or x > 3

Find undefined (singularity) points:

x = 3, x = - 3

Combine real regions and undefined points for final function domain

x < - 3 or - 1 \leq x \leq 1 or x > 3

f (x) = 8 x^{2} - 77 x + 45

f (x) = \frac{2 x ^{2} - 5 x - 12}{x ^{2} - 2 x - 8}

\frac{3 x ^{2} + 5 x - 6}{x ^{2} - 9}

f (x) = \frac{4 x}{x ( x ^{2} - 9 )}

f (x) = ∣ 2 x - 5 ∣

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