a) this is not the same problem. The second equation you suggest could have a different minimum than the first, e.g. if f(x) goes to negative infinity but only

a) this is not the same problem. The second equation you suggest could have a different minimum than the first, e.g. if f(x) goes to negative infinity but only when g(x) != 0. b) because this is a much more complex topic, for which you need to know optimization first anyways.