What happens if we graph both f and f^-1 on the same set of axes using the x-axis for the input

to both f and f^-1

[Suggestion: go desmo calculator and

type: y = x³{-21/3{-2

and y = x{-2

f and f^-1 on the same set of axes.

Suppose f:RR is a function from the set of real numbers to the same set with f(x) = x+1.

we write f² to represent f f and fⁿ⁺¹= fⁿ f.

Is it true that f² f = f f²? Why?

Is the set {g : RR \ g f = f g} infinite? Why?