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

The domain of f(x)= 2/(sqrt(|x-2|-1)) is x 3

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domain of f(x)= 2/(sqrt(|x-2|-1))

domain

f (x) = \frac{2}{∣ x - 2 ∣ - 1}

x < 1 or x > 3

Interval Notation

(- \infty, 1) \cup (3, \infty)

Solution steps

Find non-negative values for radicals:

x \leq 1 or x \geq 3

Find undefined (singularity) points:

x = 1, x = 3

Combine real regions and undefined points for final function domain

x < 1 or x > 3

\frac{1}{( 25 ) ^{x} + 4 ( 5 ^{x} ) - 1}

y = 3 (x + 7) (x + 3)

y = \frac{x - 1}{x ^{2} - x - 2}

x - 2 sin (x)

\frac{\frac{7 y ^{4}}{8}}{\frac{5 y ^{6}}{3}}

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