nth Power and nth Root of x (n odd, up to 11)

① This GeoGebra example demonstrates the graphs of y = x^n (nth power) and y = x^(1/n) (nth root) for odd integer n up to 11, showing how these two functions are inverses of each other. ② Core mathematical concepts include power functions, radical functions, domain and range for odd exponents and roots, symmetry about the line y = x, and the inverse relationship between exponentiation and root extraction. ③ Construction details: based on the summary, the applet uses text objects (text1, text2, text3) for labels, a slider or parameter a to control n, defines functions f (e.g., f(x)=x^n) and g (e.g., g(x)=x^(1/n)), and may include auxiliary objects like h or p to illustrate symmetry. ④ This is suitable for high school or early college students learning about power and root functions, inverse functions, and graphical transformations, and can be used for interactive exploration or classroom demonstration.