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

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

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domain of f(x)=(sqrt(x+5))/(x^2+3x-10)

domain

f (x) = \frac{x + 5}{x ^{2} + 3 x - 10}

- 5 < x < 2 or x > 2

Interval Notation

(- 5, 2) \cup (2, \infty)

Solution steps

Find non-negative values for radicals:

x \geq - 5

Find undefined (singularity) points:

x = 2, x = - 5

Combine real regions and undefined points for final function domain

- 5 < x < 2 or x > 2

f (x) = \frac{x + 2}{x ^{2} + 2 x - 24}

f (x) = x^{\frac{2}{3}} (x^{2} - 8)

f (x) = - (x + 1) (x - 2) (x - 3)

\frac{5}{3 x - 9}

f (x) = - 5 x + 4

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