h(x) = (x − 7)^{−1/4}

g(x) =

case f(x) = sqrt(x+4) / (x-3)

here we have:

x+4 >= 0 existence of the radical, and x-3 different from zero (division by zero is not admitted)

so the domain of f(x) is:

[-4, -3) union (-3, +infinity)

case h(x)

here we have to rquire that:

x-7 >0 only so the domain of g(x) is:

(7 , +infinity)

case g(x)

g(x) = sqrt(x+8) - 1/x

here we require:

x+8 >=0 and x different from zero, so the domain of our function is:

[-8 , 0 ) union (0 , +infinity)

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