What is the domain of (x+6)/(12-sqrt(x^2-25)) ?

The domain of (x+6)/(12-sqrt(x^2-25)) is x 13

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domain of (x+6)/(12-sqrt(x^2-25))

domain

\frac{x + 6}{12 - x ^{2} - 25}

x < - 13 or - 13 < x \leq - 5 or 5 \leq x < 13 or x > 13

Interval Notation

(- \infty, - 13) \cup (- 13, - 5] \cup [5, 13) \cup (13, \infty)

Solution steps

Find non-negative values for radicals:

x \leq - 5 or x \geq 5

Find undefined (singularity) points:

x = 13, x = - 13

Combine real regions and undefined points for final function domain

x < - 13 or - 13 < x \leq - 5 or 5 \leq x < 13 or x > 13

f (x) = \frac{2 x + 3}{5 x - 2}

f (x) = ln (x) (49 - x^{2})

f (x) = - 3 (x + 1)^{2} + 2

f (x) = \frac{x - 1}{( x + 1 ) ( x ^{2} - 3 )}

\frac{x ^{2} + 2}{3}

What is the domain of (x+6)/(12-sqrt(x^2-25)) ?
The domain of (x+6)/(12-sqrt(x^2-25)) is x<-13\lor-13<x<=-5\lor 5<= x<13\lor x>13