What is the domain of f(x)=(3x-5)/(sqrt(x^2-2x-8)) ?

The domain of f(x)=(3x-5)/(sqrt(x^2-2x-8)) is x 4

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domain of f(x)=(3x-5)/(sqrt(x^2-2x-8))

domain

f (x) = \frac{3 x - 5}{x ^{2} - 2 x - 8}

x < - 2 or x > 4

Interval Notation

(- \infty, - 2) \cup (4, \infty)

Solution steps

Find non-negative values for radicals:

x \leq - 2 or x \geq 4

Find undefined (singularity) points:

x = 4, x = - 2

Combine real regions and undefined points for final function domain

x < - 2 or x > 4

\frac{( x ^{2} + 3 x - 4 )}{x + 4}

f (x) = x - 2 - 2.6

\frac{1}{2 x ^{3}}

f (x) = \frac{3}{4} x + 12

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

What is the domain of f(x)=(3x-5)/(sqrt(x^2-2x-8)) ?
The domain of f(x)=(3x-5)/(sqrt(x^2-2x-8)) is x<-2\lor x>4