How is a power function related to a radical function?

Answer 1

You can write any radical as a power. For example, taking the square root is the same as raising to the power 1/2; taking the cubic root is the same as raising to the power 1/3. Here is an example how you can use this knowledge, to take the cubic root of 125 (which of course is 5) in Excel:= 125^(1/3)

Answer 2

The simplest example would be square and square root. You could say that they are rotated 90° from each other. Or that they reflect across the line y=x. Take the quadratic (square) function y = x^2. This is a parabola opening up. Now what if you exchange the variables, so that you have x = y^2. Now the parabola opens to the right. This could also be stated as y = sqrt(x). But typically, the square root function only returns the positive value. This would necessarily be true, if you want it to remain as a 'function' (only one y value for each x value). So you would only have a half of a parabola.

Answer 3

They are inverses of each other. Example: f'(x) = sqrt(x), x >= 0 is the inverse function of f(x) = x^2, for x >=0.