What is the domain of f(x)=(sqrt(x-3x-10))/(x^2-16) ?

The domain of f(x)=(sqrt(x-3x-10))/(x^2-16) is x<=-5

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domain of f(x)=(sqrt(x-3x-10))/(x^2-16)

domain

f (x) = \frac{x - 3 x - 10}{x ^{2} - 16}

x \leq - 5

Interval Notation

(- \infty, - 5]

Solution steps

Find non-negative values for radicals:

x \leq - 5

Find undefined (singularity) points:

x = 4, x = - 4

Combine real regions and undefined points for final function domain

x \leq - 5

- 8 x (1 - x^{2})^{3}

f (x) = (x - 3) (x + 5)

\frac{x + 3}{5 x - 1}

f (x) = 3 - 2 e x - 4

16 - 4 x

What is the domain of f(x)=(sqrt(x-3x-10))/(x^2-16) ?
The domain of f(x)=(sqrt(x-3x-10))/(x^2-16) is x<=-5