What is the domain of f(x)= 1/(sqrt(\sqrt{x-2)-1)-2} ?

The domain of f(x)= 1/(sqrt(\sqrt{x-2)-1)-2} is 3 27

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domain of f(x)= 1/(sqrt(\sqrt{x-2)-1)-2}

domain

f (x) = \frac{1}{x - 2 - 1 - 2}

3 \leq x < 27 or x > 27

Interval Notation

[3, 27) \cup (27, \infty)

Solution steps

Find non-negative values for radicals:

x \geq 3

Find undefined (singularity) points:

x = 27

Combine real regions and undefined points for final function domain

3 \leq x < 27 or x > 27

f (x) = \frac{3}{( x ^{2} - 16 )}

f (x) = \frac{1}{x + 2}

\frac{x ^{2} - 1}{x ^{3}}

ln (x - 1) + 2

\frac{1 + x}{2 - x}

What is the domain of f(x)= 1/(sqrt(\sqrt{x-2)-1)-2} ?
The domain of f(x)= 1/(sqrt(\sqrt{x-2)-1)-2} is 3<= x<27\lor x>27