A question about composite functions:
If f(x) = √x and g(x) = x^2, and you are solving for f(g(x)), ordinarily you solve for g(x) and then plug that value into f(x) to solve for f(g(x)). But what if x is a negative number? When you square it, you’ll get a positive value and then when you take the square root of that to solve for g(f(x)), the final answer will be positive only. Is that correct?

 

Yes, that’s correct. And to that I’ll add that if you look at g(f(x)), a negative number will not work.

In your graphing calculator, have a look at y=\sqrt{x^2} and compare it to y=\left(\sqrt{x}\right)^2. They’re the same when x is positive, but only one exists when it’s negative.