What is the domain of f(x)=(3x-9)/(sqrt(x^2-6x-7)) ?

The domain of f(x)=(3x-9)/(sqrt(x^2-6x-7)) is x 7

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domain of f(x)=(3x-9)/(sqrt(x^2-6x-7))

domain

f (x) = \frac{3 x - 9}{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) = lo g_{2} (8 - \frac{7 - 2 x}{3})

\frac{x - 2}{2 x + 5}

g (t) = 1 - 2^{t}

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

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

What is the domain of f(x)=(3x-9)/(sqrt(x^2-6x-7)) ?
The domain of f(x)=(3x-9)/(sqrt(x^2-6x-7)) is x<-1\lor x>7