What is the domain of f(x)= 1/((x-3)sqrt(x+3)) ?

The domain of f(x)= 1/((x-3)sqrt(x+3)) is -3 3

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domain of f(x)= 1/((x-3)sqrt(x+3))

domain

f (x) = \frac{1}{( x - 3 ) x + 3}

- 3 < x < 3 or x > 3

Interval Notation

(- 3, 3) \cup (3, \infty)

Solution steps

Find non-negative values for radicals:

x \geq - 3

Find undefined (singularity) points:

x = 3, x = - 3

Combine real regions and undefined points for final function domain

- 3 < x < 3 or x > 3

f (x) = - 2 x - 7

f (x) = (4 x - 7) (1 - 3)

f (x) = lo g_{10} (x^{2} - 7 x + 12)

f (x) = - (x - 2)^{2} + 4

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

What is the domain of f(x)= 1/((x-3)sqrt(x+3)) ?
The domain of f(x)= 1/((x-3)sqrt(x+3)) is -3<x<3\lor x>3