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

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

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

domain

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

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

Interval Notation

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

Solution steps

Find non-negative values for radicals:

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 < 1 or 1 < x \leq 2

(2.6) y = - 3 x + 7

f (x) = \frac{2 x + 1}{2}

x + 4

f (x) = \frac{20 x ^{2}}{5 x ^{2} + 3}

f (x) = 2^{x} - 5

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