One cannot have a negative under a square root, so we know 17−x≥0. Adding x to both sides yields 17≥x. Thus, x can be any number greater than or equal to 17. This gives the interval [17,∞) as our domain.
To elaborate, √n asks, "what number, when squared, gives n". Notice that positive numbers, when squared, give positive numbers. (22=4) Also, negative numbers, when squared, give positive numbers. (−22=(−2)(−2)=4) So it follows that one cannot take the square root of a negative number, since no number, when squared, yields another negative number.
When we realize that, we know that 17−x must be non-negative. This is written as the inequality 17−x≥0. Algebraic manipulation gives 17≥x, and from this we extrapolate our interval [17,∞].
