What is the domain of (sqrt(x-1)+2)/(sqrt(x-1)-2) ?

The domain of (sqrt(x-1)+2)/(sqrt(x-1)-2) is 1 5

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domain of (sqrt(x-1)+2)/(sqrt(x-1)-2)

domain

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

1 \leq x < 5 or x > 5

Interval Notation

[1, 5) \cup (5, \infty)

Solution steps

Find non-negative values for radicals:

x \geq 1

Find undefined (singularity) points:

x = 5

Combine real regions and undefined points for final function domain

1 \leq x < 5 or x > 5

f (x) = 2 - 2 x

f (x) = 8 x - ln (8 x)

f (x) = 7 x^{\frac{1}{4}} + 10

\frac{1}{x ^{2} - 4}

f (x) = \frac{( t ^{2} - 6 t )}{t ^{4} - 1296}

What is the domain of (sqrt(x-1)+2)/(sqrt(x-1)-2) ?
The domain of (sqrt(x-1)+2)/(sqrt(x-1)-2) is 1<= x<5\lor x>5