What is the domain of f(x)=(sqrt(x^5-32))/(x-3) ?

The domain of f(x)=(sqrt(x^5-32))/(x-3) is 2 3

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domain of f(x)=(sqrt(x^5-32))/(x-3)

domain

f (x) = \frac{x ^{5} - 32}{x - 3}

2 \leq x < 3 or x > 3

Interval Notation

[2, 3) \cup (3, \infty)

Solution steps

Find non-negative values for radicals:

x \geq 2

Find undefined (singularity) points:

x = 3

Combine real regions and undefined points for final function domain

2 \leq x < 3 or x > 3

3 x - 2

x^{3} - 6 x^{2} + 9 x - 4

(3 - x) (- 7 - x)

y = \frac{5}{3} x - 2

\frac{x ^{2}}{x ^{2} + 8}

What is the domain of f(x)=(sqrt(x^5-32))/(x-3) ?
The domain of f(x)=(sqrt(x^5-32))/(x-3) is 2<= x<3\lor x>3