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

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

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domain of ([sqrt(2-x)])/([sqrt(x^2-1)])

domain

\frac{[ 2 - x ]}{[ x ^{2} - 1 ]}

x < - 1 or 1 < x \leq 2

Interval Notation

(- \infty, - 1) \cup (1, 2]

Solution steps

Find non-negative values for radicals:

x \leq - 1 or 1 \leq x \leq 2

Find undefined (singularity) points:

x = 1, x = - 1

Combine real regions and undefined points for final function domain

x < - 1 or 1 < x \leq 2

f (x) = \frac{x - 8}{x ( x - 9 )}

3 y + 6 x = 9

1 (x + 4)^{2} - 2

y = x^{2} + \frac{48}{5}

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

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