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

The domain of 1/(sqrt(ln((x-1)^2)-1)) is x sqrt(e)+1

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domain of 1/(sqrt(ln((x-1)^2)-1))

domain

\frac{1}{ln ( ( x - 1 ) ^{2} ) - 1}

x < - e + 1 or x > e + 1

Interval Notation

(- \infty, - e + 1) \cup (e + 1, \infty)

Solution steps

Find non-negative values for radicals:

x \leq - e + 1 or x \geq e + 1

Find undefined (singularity) points:

x = e + 1, x = - e + 1

Combine real regions and undefined points for final function domain

x < - e + 1 or x > e + 1

f (x) = \frac{4}{x + 1} + 5

f (x) = 8 x^{2} - x^{4}

f (x) = 72 - x^{2} + x

f (x) = \frac{x - 3 x - 10}{x ^{2} - 16}

- 8 x (1 - x^{2})^{3}

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