What is the domain of f(x)=(sqrt(x)+2)/(x^6-64) ?

The domain of f(x)=(sqrt(x)+2)/(x^6-64) is 0 2

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domain of f(x)=(sqrt(x)+2)/(x^6-64)

domain

f (x) = \frac{x + 2}{x ^{6} - 64}

0 \leq x < 2 or x > 2

Interval Notation

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

Solution steps

Find non-negative values for radicals:

x \geq 0

Find undefined (singularity) points:

x = 2, x = - 2

Combine real regions and undefined points for final function domain

0 \leq x < 2 or x > 2

(\frac{3}{2}, \frac{4}{3}), (3, - 2)

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

(8, 4), (4, 2)

(0, 4), (7, 8)

(- 5, 4), (1, - 3)

What is the domain of f(x)=(sqrt(x)+2)/(x^6-64) ?
The domain of f(x)=(sqrt(x)+2)/(x^6-64) is 0<= x<2\lor x>2