What is the domain of f(x)=(sqrt(9+5x))/(x^2-16) ?

The domain of f(x)=(sqrt(9+5x))/(x^2-16) is -9/5 4

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domain of f(x)=(sqrt(9+5x))/(x^2-16)

domain

f (x) = \frac{9 + 5 x}{x ^{2} - 16}

- \frac{9}{5} \leq x < 4 or x > 4

Interval Notation

[- \frac{9}{5}, 4) \cup (4, \infty)

Solution steps

Find non-negative values for radicals:

x \geq - \frac{9}{5}

Find undefined (singularity) points:

x = 4, x = - 4

Combine real regions and undefined points for final function domain

- \frac{9}{5} \leq x < 4 or x > 4

What is the domain of f(x)=(sqrt(9+5x))/(x^2-16) ?
The domain of f(x)=(sqrt(9+5x))/(x^2-16) is -9/5 <= x<4\lor x>4