Question

State the domain: g(x)=-2+the square root of (1-x). Please explain how I get the answer.

Answer 1

First of all, thanks for using parentheses. Your doing so made the problem so much clearer than it would have been otherwise.

g(x) = -2 + √(1-x).

What's the domain of this function? Focus on √(1-x). Recall that the domain of the square root function is [0, infinity); in other words, the domain consists of the set of all real numbers equal to or greater than zero (0).

What's the domain of √(1-x)?

Borrowing the comments above, (1-x) must be ≥ 0.

Let's solve this inequality: Add x to both sides. We get 1 - x + x ≥ 0 + x.

Then x ≤ 1 is the domain of the given function.