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

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

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