What is the domain of h(x)=(9x)/(x(x^2-36)) ?

The domain of h(x)=(9x)/(x(x^2-36)) is x 6

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domain of h(x)=(9x)/(x(x^2-36))

domain

h (x) = \frac{9 x}{x ( x ^{2} - 36 )}

x < - 6 or - 6 < x < 0 or 0 < x < 6 or x > 6

Interval Notation

(- \infty, - 6) \cup (- 6, 0) \cup (0, 6) \cup (6, \infty)

Solution steps

Find undefined (singularity) points:

x = 0, x = - 6, x = 6

The function domain

x < - 6 or - 6 < x < 0 or 0 < x < 6 or x > 6

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

g (x) = g (x) = {x + 2, x \geq 3}

f (x) = ln (\frac{1}{( x ^{2} - 3 x - 28 )})

x^{2} - 4 x

x 8 - x^{2}

What is the domain of h(x)=(9x)/(x(x^2-36)) ?
The domain of h(x)=(9x)/(x(x^2-36)) is x<-6\lor-6<x<0\lor 0<x<6\lor x>6