Which of the following is a representation of the domain of the expression:

Question

h(x) = 12x + 3 / 2 - square root over x

a)[0,4)

b) [(0,4) U ( 4, infinity)

I know that the answer is b, but how do I come to this answer?

Answer 1

x cannot be negative (because the square roots of negatove numbers are unreal) and it also cannot cause the denomimator (2 - sqrt x) to be zero. Therefore x cannot be exactly 4, either.