What is the domain of f(x)= 1/(6(sqrt(2x+16))-12) ?

The domain of f(x)= 1/(6(sqrt(2x+16))-12) is -8 -6

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domain of f(x)= 1/(6(sqrt(2x+16))-12)

domain

f (x) = \frac{1}{6 ( 2 x + 16 ) - 12}

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

Interval Notation

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

Solution steps

Find non-negative values for radicals:

x \geq - 8

Find undefined (singularity) points:

x = - 6

Combine real regions and undefined points for final function domain

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

\frac{x}{tan ( x )}

f (x) = \frac{2 - x}{4 ( x - 5 )}

\frac{2 x}{x ^{2} - 1}

2 x + 3 y = 9

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

What is the domain of f(x)= 1/(6(sqrt(2x+16))-12) ?
The domain of f(x)= 1/(6(sqrt(2x+16))-12) is -8<= x<-6\lor x>-6