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

The domain of (2x-6)/(sqrt(x^2+7)-4) is x 3

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

domain

\frac{2 x - 6}{x ^{2} + 7 - 4}

x < - 3 or - 3 < x < 3 or x > 3

Interval Notation

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

Solution steps

Find non-negative values for radicals:

- \infty < x < \infty

Find undefined (singularity) points:

x = 3, x = - 3

Combine real regions and undefined points for final function domain

x < - 3 or - 3 < x < 3 or x > 3

\frac{1}{x - 1} - 1

f (x) = \frac{x ^{3} - 2 x ^{2} - 3 x}{2 x ^{2} - x - 6}

f (x) = (x + 3)^{2} + (y + 6)^{2} = 16

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

f (x) = ln ∣ x - 1 ∣

What is the domain of (2x-6)/(sqrt(x^2+7)-4) ?
The domain of (2x-6)/(sqrt(x^2+7)-4) is x<-3\lor-3<x<3\lor x>3