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

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

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

domain

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

- 3 \leq x < - 2 or - 2 < x < 5 or x > 5

Interval Notation

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

Solution steps

Find non-negative values for radicals:

x \geq - 3

Find undefined (singularity) points:

x = - 2, x = 5

Combine real regions and undefined points for final function domain

- 3 \leq x < - 2 or - 2 < x < 5 or x > 5

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

x^{\frac{5}{3}} - 5 x^{\frac{2}{3}}

f (x) = x^{2} - 8 x + 9

f (x) = x^{2} - 8 x + 7

f (x) = 5 - 3 x

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