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

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

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

domain

f (x) = \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) = 30 x + 40

y = \frac{4}{9} x - 1

f (x) = - 3 x + 6

f (x) = - 3 x + 3

g (x) = \frac{5 x + 3 - x ^{2}}{3}

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