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

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

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

domain

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

x < - 1 or - 1 < x < 1 or x > 1

Interval Notation

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

Solution steps

Find non-negative values for radicals:

- \infty < x < \infty

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 x > 1

f (x) = x^{2} - 3, x \geq 0

\frac{3 x + 4}{2 x - 3}

f (x) = 2 x + 9

f (x) = \frac{( x + 2 ) ( x - 4 )}{( x + 3 ) ( x - 4 )}

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