What is the domain of f(x)=(4x)/(sqrt(x^2-6x-7)) ?

The domain of f(x)=(4x)/(sqrt(x^2-6x-7)) is x 7

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domain of f(x)=(4x)/(sqrt(x^2-6x-7))

domain

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

\frac{3 x ^{2} - 9}{x - 1}

f (x) = ∣ x + 2 ∣ - 1, - 4 < x < 0

f (x) = 3 x^{2} + 6 - 4

f (x) = 2 + lo g_{2} (x)

What is the domain of f(x)=(4x)/(sqrt(x^2-6x-7)) ?
The domain of f(x)=(4x)/(sqrt(x^2-6x-7)) is x<-1\lor x>7