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

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

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

domain

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

\frac{1 - 33}{2} < x < 0 or x > \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 x \leq 0 or x \geq \frac{1 + 33}{2}

Find undefined (singularity) points:

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

Combine real regions and undefined points for final function domain

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

f (x) = 3 x^{2} - 2 x + 1

f (x) = 18 - 3 x - x^{2}

y = x - 7

f (x) = 3 csc (x) + 2

- 8 x

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