One cannot have a negative under a square root, so we know 17 - x >= 017−x≥0. Adding xx to both sides yields 17 >= x17≥x. Thus, xx can be any number greater than or equal to 1717. This gives the interval [17, infty)[17,∞) as our domain.
To elaborate, sqrt(n)√n asks, "what number, when squared, gives nn". Notice that positive numbers, when squared, give positive numbers. (2^2 = 422=4) Also, negative numbers, when squared, give positive numbers. (-2^2 = (-2)(-2) = 4−22=(−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 - x17−x must be non-negative. This is written as the inequality 17 - x >= 017−x≥0. Algebraic manipulation gives 17 >= x17≥x, and from this we extrapolate our interval [17, infty][17,∞].
