What is the domain of f(x)=(x^2-1)/(sqrt(x^2+2x-15)) ?

The domain of f(x)=(x^2-1)/(sqrt(x^2+2x-15)) is x 3

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domain of f(x)=(x^2-1)/(sqrt(x^2+2x-15))

domain

f (x) = \frac{x ^{2} - 1}{x ^{2} + 2 x - 15}

x < - 5 or x > 3

Interval Notation

(- \infty, - 5) \cup (3, \infty)

Solution steps

Find non-negative values for radicals:

x \leq - 5 or x \geq 3

Find undefined (singularity) points:

x = 3, x = - 5

Combine real regions and undefined points for final function domain

x < - 5 or x > 3

f (x) = - 2 (x + 1)^{2} + 4

f (x) = \frac{x - 4}{x - 2}

f (x) = 15 x - 3

\frac{1}{x ^{2} ( x + 1 )}

f (x) = \frac{8}{x + 1}

What is the domain of f(x)=(x^2-1)/(sqrt(x^2+2x-15)) ?
The domain of f(x)=(x^2-1)/(sqrt(x^2+2x-15)) is x<-5\lor x>3