What is the domain of f(x)= 1/(sqrt(x^2-6x-7)) ?

The domain of f(x)= 1/(sqrt(x^2-6x-7)) is x 7

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domain of f(x)= 1/(sqrt(x^2-6x-7))

domain

f (x) = \frac{1}{x ^{2} - 6 x - 7}

x < - 1 or x > 7

Interval Notation

(- \infty, - 1) \cup (7, \infty)

Solution steps

Find non-negative values for radicals:

x \leq - 1 or x \geq 7

Find undefined (singularity) points:

x = 7, x = - 1

Combine real regions and undefined points for final function domain

x < - 1 or x > 7

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

\frac{x ^{2} - 11 x + 18}{x ^{2} + 2 x - 8}

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

f (x) = \frac{5 x}{x ^{2} + 81}

7 x^{2} - 7 x

What is the domain of f(x)= 1/(sqrt(x^2-6x-7)) ?
The domain of f(x)= 1/(sqrt(x^2-6x-7)) is x<-1\lor x>7