What is the domain of f(x)=sqrt((x+3)/(x^2-36)) ?

The domain of f(x)=sqrt((x+3)/(x^2-36)) is -6 6

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domain of f(x)=sqrt((x+3)/(x^2-36))

domain

f (x) = \frac{x + 3}{x ^{2} - 36}

- 6 < x \leq - 3 or x > 6

Interval Notation

(- 6, - 3] \cup (6, \infty)

Solution steps

Find non-negative values for radicals:

- 6 < x \leq - 3 or x > 6

Find undefined (singularity) points:

x = 6, x = - 6

Combine real regions and undefined points for final function domain

- 6 < x \leq - 3 or x > 6

f (x) = 14 - x + 14 + x

\frac{1 - 9 x}{5 x + 4}

f (x) = \frac{( 6 t - 1 )}{t ^{2} + 7}

What is the domain of f(x)=sqrt((x+3)/(x^2-36)) ?
The domain of f(x)=sqrt((x+3)/(x^2-36)) is -6<x<=-3\lor x>6