Inverse Functions in Algebra

Question

Hey, would anyone help me with this inverse function exercise? I have no idea what to do.

1. Suppose  is a function from the set of real numbers to the same set with . We write  to represent  and . Is it true that ? Why? Is the set { l } infinite? Why? 

1. 2 What happens if we graph both  and  on the same set of axes, using the x-axis for the input to both  and  ? 

1. 3 Go to www.desmos.com/calculator and type  {-2 < x < 2},  {–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  and  on the same set of axes.

Answer 1

f2 = f comp f = x+1+1 = x+2

f2 comp f = x+1+2 = x+3

f comp f2 = x+2+1 = x+3, so yes they are the same...

f3 = f2 comp f = x+3

f4 = f3 comp f = x+4

...

Suppose Fn = x+n

F(n+1) = Fn comp f = x+1+n = x+(n+1)

so the pattern hold by induction

F comp Finv = x so when you graph them on

the same plot, they shall be SYMMETRIC about

the line y=x