What is the domain of f(x)=(sqrt(x+9))/((x+4)(x-8)) ?

The domain of f(x)=(sqrt(x+9))/((x+4)(x-8)) is -9 8

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domain of f(x)=(sqrt(x+9))/((x+4)(x-8))

domain

f (x) = \frac{x + 9}{( x + 4 ) ( x - 8 )}

- 9 \leq x < - 4 or - 4 < x < 8 or x > 8

Interval Notation

[- 9, - 4) \cup (- 4, 8) \cup (8, \infty)

Solution steps

Find non-negative values for radicals:

x \geq - 9

Find undefined (singularity) points:

x = - 4, x = 8

Combine real regions and undefined points for final function domain

- 9 \leq x < - 4 or - 4 < x < 8 or x > 8

What is the domain of f(x)=(sqrt(x+9))/((x+4)(x-8)) ?
The domain of f(x)=(sqrt(x+9))/((x+4)(x-8)) is -9<= x<-4\lor-4<x<8\lor x>8