What is the domain of f(x)=sqrt((x+8)/((x-4)(x+6))) ?

The domain of f(x)=sqrt((x+8)/((x-4)(x+6))) is -8 4

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domain of f(x)=sqrt((x+8)/((x-4)(x+6)))

domain

f (x) = \frac{x + 8}{( x - 4 ) ( x + 6 )}

- 8 \leq x < - 6 or x > 4

Interval Notation

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

Solution steps

Find non-negative values for radicals:

- 8 \leq x < - 6 or x > 4

Find undefined (singularity) points:

x = 4, x = - 6

Combine real regions and undefined points for final function domain

- 8 \leq x < - 6 or x > 4

\frac{2 x - 3}{x + 1}

\frac{x - 4}{2 x ^{2} + 8 x}

\frac{3 x - 2}{x + 5}

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

\frac{1}{x + 9} + 3

What is the domain of f(x)=sqrt((x+8)/((x-4)(x+6))) ?
The domain of f(x)=sqrt((x+8)/((x-4)(x+6))) is -8<= x<-6\lor x>4