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Use set or interval notation to give the domain of each of the functions: h(x)=`sqrt(x^2 - 16)/(x + x^2)` f(x)=`(x^3-8)/(x^2+2x-8)` g(x)=`(x-5)/(sin x)`

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The domain of the following function has to be determined. The domain of a function f(x) is all the real values of x for which f(c) is real.

h(x) = `sqrt(x^2-16)/(x+x^2)`

h(x is real for all real values of x such that `x + x^2 != 0`

=> `x(x + 2) != 0`

=> `x!= 0` and `x != -2`

The domain of the function is `R - {0, -2}`

 f(x) = `(x^3 - 8)/(x^2 + 2x - 8)`

=> f(x) = `(x^3 - 8)/((x - 2)(x + 4))`

The domain of the function is `R - {2, -4}`

g(x) = `(x - 5)/ (sin x)`

The domain of the function is `R - {n*2*pi, pi + n*2*pi}` where n is an integer.

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