What is the domain of f(x)=\sqrt[3]{x/(x-4)} ?

The domain of f(x)=\sqrt[3]{x/(x-4)} is x 4

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domain of f(x)=\sqrt[3]{x/(x-4)}

domain

x < 4 or x > 4

Interval Notation

(- \infty, 4) \cup (4, \infty)

Solution steps

Find undefined (singularity) points:

x = 4

The function domain

x < 4 or x > 4

\frac{3}{2} x + 3

\frac{x}{5 x - 2}

f (x) = x + 2 x + 6 = 9

- \frac{1}{3} x + 5

f (x) = \frac{7 x}{x - 6}

What is the domain of f(x)=\sqrt[3]{x/(x-4)} ?
The domain of f(x)=\sqrt[3]{x/(x-4)} is x<4\lor x>4