Find the domain of the function `h(x)=(x-3)/(x^3-64x)`

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The domain of `h(x)= (x-3)/(x^3-64x)` has to be determined. The domain is the set of values that x belongs to for which h(x) is real and defined.

`h(x) = (x-3)/(x^3-64x) `

x^3 - 64x can take all values except 0.

`x^3 - 64x != 0`

=> `x^2 != 64`

=> `x!= 8` and `x!= -8` and `x != 0`

The domain of h(x) is R - {-8, 0, 8}

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