Describe in detail the relationships between the three curves.

\fWe want to graph both f and f" on the same set of axes. To start, go to www.desmos.comlcalculator and type in y = 3 {2 s x s 2}, y = 31/3132 5 x S 2}, and y = 1' {2 S X S 2}. Describe in detail the relationships between the three curves. Now, post your own example. Give your function, its inverse. and graph both your function and its inverse function on the same axes. What line is the line of symmetry of your function and its inverse? Graph that line in your example. Now, find (f-f")(z) and (f'i-fmr) . How does your answer compare with the equation of the line of symmetry you found? Explain. Discuss the process of graphing both f and f\" on the same set of axes. What line must be the line of symmetry for any function and its inverse? Why? Explain. Next, let f: R > R be a function from the set of real numbers to the set of real numbers, where f(x) = 3x 5 . What is f\"? Graph both f and f\" on the same BXES. There is an algebra offunctions, where we write f2 to represent f o f. Is it true that f2 o f = f 0 f2? Show why or why not using an example function that you make up. Explain your answer showing every step