What is the domain of f(x)=(sqrt(4-x^2))/(x^2-1) ?

The domain of f(x)=(sqrt(4-x^2))/(x^2-1) is -2<= x<-1\lor-1<x<1\lor 1<x<= 2

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domain of f(x)=(sqrt(4-x^2))/(x^2-1)

domain

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

Interval Notation

Solution steps

Find non-negative values for radicals:

- 2 \leq x \leq 2

Find undefined (singularity) points:

x = 1, x = - 1

Combine real regions and undefined points for final function domain

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

What is the domain of f(x)=(sqrt(4-x^2))/(x^2-1) ?
The domain of f(x)=(sqrt(4-x^2))/(x^2-1) is -2<= x<-1\lor-1<x<1\lor 1<x<= 2