Answer to Question #125820 in Algebra for Dani wagas

Question

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 to www.desmos.com/calculator and type y=x^3 {-2 < x < 2}, y=x^{1/3} {–2 < x < 2}, and y = x {–2 < x < 2}, and describe the relationship between the three curves.] Then post your own example discussing the difficulty of graph both f and f^{-1} on the same set of axes.

Suppose f:R \rightarrow R is a function from the set of real numbers to the same set with f(x)=x+1. We write f^{2} to represent f \circ f and f^{n+1}=f^n \circ f. Is it true that f^2 \circ f = f \circ f^2? Why? Is the set {g:R \rightarrow R l g \circ f=f \circ g} infinite? Why?

Answer 1

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