Question 513411
Work from the outside in.  The function g(x) is a composition of functions: first you take x and find 1 - x, then you take the square root of 1 - x.  Each layer of this function has a natural domain (possible set of inputs) and range (possible set of outputs).  The trick here is to look at the outermost layer first and see what sorts of inputs can go inside of it.  

In this case, the outermost layer is sqrt(u) (where u represents the inside, i.e., u = 1 - x).  What sorts of u can we take the square root of and get back a real number?  The answer is that u must be a non-negative real number.  Written as a formula, we get:

u >= 0  (where >= means "greater than or equal")

Now we recall that u was the inside of this composition of functions: u = 1 - x.  Thus our inequality becomes:

1 - x >= 0
1 >= x (adding x to both sides)
x <= 1 (flipping both the left and right hand sides AND the inequality)

So for u to be a valid input into sqrt(u), x must be less than or equal to 1.  This corresponds to all numbers in the interval (-infinity, 1], or choice (a).