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

The domain of f(x)=(sqrt(x^2-3))/(ln(x^2-3)) is x 2

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domain of f(x)=(sqrt(x^2-3))/(ln(x^2-3))

domain

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

x < - 2 or - 2 < x < - 3 or 3 < x < 2 or x > 2

Interval Notation

(- \infty, - 2) \cup (- 2, - 3) \cup (3, 2) \cup (2, \infty)

Solution steps

Find non-negative values for radicals:

x \leq - 3 or x \geq 3

Find positive values for logs:

x < - 3 or x > 3

Find undefined (singularity) points:

x = 2, x = - 2

Combine real regions and undefined points for final function domain

x < - 2 or - 2 < x < - 3 or 3 < x < 2 or x > 2

- x + 5

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

f (x) = \frac{1}{2} x - \frac{6}{x}

f (x) = 4 + 2 x - 3

\frac{x + 6}{2}

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