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

The domain of (sqrt(3-x))/(sqrt(x^2-1)) is x<-1\lor 1<x<= 3

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

domain

\frac{3 - x}{x ^{2} - 1}

x < - 1 or 1 < x \leq 3

Interval Notation

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

Solution steps

Find non-negative values for radicals:

x \leq - 1 or 1 \leq x \leq 3

Find undefined (singularity) points:

x = 1, x = - 1

Combine real regions and undefined points for final function domain

x < - 1 or 1 < x \leq 3

(1 - \frac{3}{x})^{x}

f (x) = x + ln (x)

f (x) = ∣ 2 x - 1 ∣

f (x) = ln ((\frac{9 - x}{2 x + 3})^{\frac{1}{3}})

f (x) = \frac{3 x ^{2}}{x ^{2} + 2 x - 35}

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