## Related questions with answers

Question

Find the domain of each function. Write answers using interval notation. $f(x)=\sqrt{\frac{-1}{x^{3}-1}}$

Solution

VerifiedAnswered 1 year ago

Answered 1 year ago

Step 1

1 of 4The function, $f(x) = \sqrt{\dfrac{-1}{x^3 -1}}$, is a radical expression. This means, that $f(x)$ is only defined when the radicand, $\dfrac{-1}{x^3 -1}\geq 0$.

Notice that $\dfrac{-1}{x^3 -1}$ can never be equal to zero because the numerator is a constant of -1. Hence, we will only solve for

$\dfrac{-1}{x^3 -1} >0$

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