What is the domain of f(x)=(sqrt(9-x^2))/(x^3-x) ?

The domain of f(x)=(sqrt(9-x^2))/(x^3-x) is -3<= x<-1\lor-1<x<0\lor 0<x<1\lor 1<x<= 3

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domain of f(x)=(sqrt(9-x^2))/(x^3-x)

domain

f (x) = \frac{9 - x ^{2}}{x ^{3} - x}

- 3 \leq x < - 1 or - 1 < x < 0 or 0 < x < 1 or 1 < x \leq 3

Interval Notation

[- 3, - 1) \cup (- 1, 0) \cup (0, 1) \cup (1, 3]

Solution steps

Find non-negative values for radicals:

- 3 \leq x \leq 3

Find undefined (singularity) points:

x = 0, x = - 1, x = 1

Combine real regions and undefined points for final function domain

- 3 \leq x < - 1 or - 1 < x < 0 or 0 < x < 1 or 1 < x \leq 3

arcsin (e^{3 x})

f (x) = \frac{2 x - 1}{3 - 2 x}

6 x^{2} - 13 x + 5

f (x) = ∣ 3 x - 5 ∣ - 2 x + 2

What is the domain of f(x)=(sqrt(9-x^2))/(x^3-x) ?
The domain of f(x)=(sqrt(9-x^2))/(x^3-x) is -3<= x<-1\lor-1<x<0\lor 0<x<1\lor 1<x<= 3