How to solve for the inverse of a function?

[KLscilevothma]

Let f:[rr]--> [rr]

It isn't a homework problem.
Let f:[rr]--> [rr] be a function such that f(xy)=f(x)+f(y) for all x,y belong to real numbers
a) Show that for all integers n, f(xⁿ)=nf(x)
b) Suppose the inverse of f exists. Show that for all integers n, [f^-1(x)]ⁿ=f^-1(nx)

I know how to do part (a) but not part (b). Could someone please give me some hints/solution. I can't do problems involving "inverse of a function" unless they are very simple, like to find f^-1 of f(x)=(1-x)/(1+x) where x does not equal to 1 or -1

 

[Dx]

Originally posted by KL Kam
It isn't a homework problem.
Let f:[rr]--> [rr] be a function such that f(xy)=f(x)+f(y) for all x,y belong to real numbers
a) Show that for all integers n, f(xⁿ)=nf(x)
b) Suppose the inverse of f exists. Show that for all integers n, [f^-1(x)]ⁿ=f^-1(nx)

I know how to do part (a) but not part (b). Could someone please give me some hints/solution. I can't do problems involving "inverse of a function" unless they are very simple, like to find f^-1 of f(x)=(1-x)/(1+x) where x does not equal to 1 or -1

a) that's the power rule formula for solving dx
b) this is antidx. remember its the opposite of dx. if your good with the power rule just do it backwards and subtract.

A good http://math.vanderbilt.edu/~pscrooke/toolkit.shtml for you to use.
dx

 

[mathman]

inverse

Let x=f(y), or y=f^-1(x)
f(yⁿ)=nf(y)=nx
Take inverse on both sides and get
yⁿ=(f^-1(x))ⁿ=f^-1(nx)