What is the domain of f(x)=(5t-1)/(sqrt(t^3-t^2-8t)) ?

The domain of f(x)=(5t-1)/(sqrt(t^3-t^2-8t)) is (1-sqrt(33))/2 (1+sqrt(33))/2

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domain of f(x)=(5t-1)/(sqrt(t^3-t^2-8t))

domain

f (x) = \frac{5 t - 1}{t ^{3} - t ^{2} - 8 t}

\frac{1 - 33}{2} < t < 0 or t > \frac{1 + 33}{2}

Interval Notation

(\frac{1 - 33}{2}, 0) \cup (\frac{1 + 33}{2}, \infty)

Solution steps

Find non-negative values for radicals:

\frac{1 - 33}{2} \leq t \leq 0 or t \geq \frac{1 + 33}{2}

Find undefined (singularity) points:

t = 0, t = \frac{1 + 33}{2}, t = \frac{1 - 33}{2}

Combine real regions and undefined points for final function domain

\frac{1 - 33}{2} < t < 0 or t > \frac{1 + 33}{2}

f (x) = 8 x^{3} - 12 x^{2} + 4

(5 - x)^{4}

(1, 5), (2, 7)

\frac{x - 2}{3 x + 5}

\frac{4}{x} + x^{4}

What is the domain of f(x)=(5t-1)/(sqrt(t^3-t^2-8t)) ?
The domain of f(x)=(5t-1)/(sqrt(t^3-t^2-8t)) is (1-sqrt(33))/2 <t<0\lor t>(1+sqrt(33))/2