If x is any real number, then x^2 is non-negative and so sqrt(x) is defined. yes, the domain is all real numbers. Since sqrt(x) is defined as thenon-negativenumber, a, such that a^2= x, the range is all non-negative numbers, as you say. What is the book's answer?

No, the algebra does NOT simplify to x. Since there are two numbers, positive and negative that give the same square, and sqrt only returns the positive one, sqrt(x^2) simplifies to |x|.Also, when looking at the composition of g(f(x)), the algebra simplifies to x.

However, if you graph by plugging into g(x) and then into f(x), you get the absolute value of x. What gives?

Thanks.

Bret Norvilitis

OPHS