What is the domain of f(x)=sqrt((x^2-1)/(x^3-8)) ?

The domain of f(x)=sqrt((x^2-1)/(x^3-8)) is -1 2

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domain of f(x)=sqrt((x^2-1)/(x^3-8))

domain

f (x) = \frac{x ^{2} - 1}{x ^{3} - 8}

- 1 \leq x \leq 1 or x > 2

Interval Notation

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

Solution steps

Find non-negative values for radicals:

- 1 \leq x \leq 1 or x > 2

Find undefined (singularity) points:

x = 2

Combine real regions and undefined points for final function domain

- 1 \leq x \leq 1 or x > 2

\frac{1}{2} x^{2}

x^{3} + 4

f (x) = f (t) = - 16 t^{2} + 16 t + 32

f (x) = x^{3} + 3 x^{2} - 2

f (x) = \frac{82}{( 1 - 9 x ) ^{2}}

What is the domain of f(x)=sqrt((x^2-1)/(x^3-8)) ?
The domain of f(x)=sqrt((x^2-1)/(x^3-8)) is -1<= x<= 1\lor x>2