What is the domain of ((x+4))/((4-sqrt(x^2-9))) ?

The domain of ((x+4))/((4-sqrt(x^2-9))) is x 5

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domain of ((x+4))/((4-sqrt(x^2-9)))

domain

\frac{( x + 4 )}{( 4 - x ^{2} - 9 )}

x < - 5 or - 5 < x \leq - 3 or 3 \leq x < 5 or x > 5

Interval Notation

(- \infty, - 5) \cup (- 5, - 3] \cup [3, 5) \cup (5, \infty)

Solution steps

Find non-negative values for radicals:

x \leq - 3 or x \geq 3

Find undefined (singularity) points:

x = 5, x = - 5

Combine real regions and undefined points for final function domain

x < - 5 or - 5 < x \leq - 3 or 3 \leq x < 5 or x > 5

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

f (x) = lo g_{10} (\frac{1}{3}) x

138.79 \cdot \frac{1}{x ^{0.991}}

\frac{x - 3}{x - 6}

x^{8}

What is the domain of ((x+4))/((4-sqrt(x^2-9))) ?
The domain of ((x+4))/((4-sqrt(x^2-9))) is x<-5\lor-5<x<=-3\lor 3<= x<5\lor x>5