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

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

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

domain

\frac{- x + 3}{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 < - 1 or 1 < 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

x^{2} - x - 6

(- 2, - 4), (4, 4)

6 x - 3 y = 9

f (x) = 5 x - 3

f (x) = x^{4} + 7

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