HERE THE ACTIVITY
I'd like to help, but I don't think you copied the questions down well enough for people to understand what needs to be found.
For example, there's a reference to a table, but you didn't copy the table. Also, it's not entirely clear whether f(x)=(x-1)^(1/2) or f(x)=x^(1/2)-1. And then in point 2 you redefine f(x) using cube roots, but normally a textbook or worksheet would use a different letter to avoid confusion, since we already used f(x) to mean something else.
Also the question "when will g(x)=x-1 be a function" doesn't seem to make much sense, since that is always a function, for all real x.
Would it be possible to take a picture of the problem and upload using, say, tinypic.com?
OK, I see the worksheet itself is a little hard to understand the way it's written, but I'll try to answer:
a) is a function for all real x. This could be written in several different ways, including and .
b)
Greater than zero:
Less than zero:
Equal to zero:
c) The domain of is . This corresponds to .
Follow up question: is a function for because all real numbers have exactly one real cube root. Thus as long as is a real number, will associate it with a unique value. The range is also all real numbers.
Integrative Activity: For a function , the domain of is described by .