What is the domain of 3/(sqrt(x+4))-ln(x^2-x-6) ?

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

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domain of 3/(sqrt(x+4))-ln(x^2-x-6)

domain

\frac{3}{x + 4} - ln (x^{2} - x - 6)

- 4 < x < - 2 or x > 3

Interval Notation

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

Solution steps

Find non-negative values for radicals:

x \geq - 4

Find positive values for logs:

x < - 2 or x > 3

Find undefined (singularity) points:

x = - 4

Combine real regions and undefined points for final function domain

- 4 < x < - 2 or x > 3

(- 3, - 3), (2, 9)

(5.5) (- 3.3)

f (2) = 2 x + 1

(8.2) (18.4)

f (x) = x - 6

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