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

f (x) = \frac{4 - x ^{2}}{x ^{2} - 1}

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

Interval Notation

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

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

y = 2 x - 6

f (x) = 2 x^{2} - 4 x + 5, 0 \leq x \leq 7

(5.4) (4.3)

f (x) = \frac{10 - 3 x}{2}

f (x) = x + x + 10

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