What is the domain of (ln(x+3))/(sqrt(x^2-1)) ?

The domain of (ln(x+3))/(sqrt(x^2-1)) is -3 1

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domain of (ln(x+3))/(sqrt(x^2-1))

domain

\frac{ln ( x + 3 )}{x ^{2} - 1}

- 3 < x < - 1 or x > 1

Interval Notation

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

Solution steps

Find non-negative values for radicals:

x \leq - 1 or x \geq 1

Find positive values for logs:

x > - 3

Find undefined (singularity) points:

x = 1, x = - 1

Combine real regions and undefined points for final function domain

- 3 < x < - 1 or x > 1

f (x) = 4 + 5 x

f (x) = \frac{3 x ^{2} - 2 x - 8}{2 x ^{2} + 3 x - 10}

f (x) = x + 4 x^{2} + 6 x - 55

2 (x + 6)^{2} + 5

lo g_{\frac{1}{2}} (- x) - 4

What is the domain of (ln(x+3))/(sqrt(x^2-1)) ?
The domain of (ln(x+3))/(sqrt(x^2-1)) is -3<x<-1\lor x>1