Hi everyone,

I've just encountered a tricky inverse question. Can someone please give me a hint.

Assume that f and g are both one-to-one functions. Express (f of g )^(-1) in terms of f^(-1) and g^(-1).

Thanks a lot everyone.

Printable View

- November 20th 2011, 09:28 PMpohkidTricky inverse question
Hi everyone,

I've just encountered a tricky inverse question. Can someone please give me a hint.

Assume that f and g are both one-to-one functions. Express (f of g )^(-1) in terms of f^(-1) and g^(-1).

Thanks a lot everyone. - November 21st 2011, 03:36 AMAmerRe: Tricky inverse question
you should know that for any function f ,f^-1 of f has the property f(f^-1)(x) = x or f^-1(f(x)) = x

so suppose that "h " is the inverse function of now just find "h" such that

can you handle it ?

take inverse function of "f" then for "g" - November 21st 2011, 04:39 AMPlatoRe: Tricky inverse question
- November 21st 2011, 06:24 AMDevenoRe: Tricky inverse question
another way to look at this is:

g:x-->y f:y-->z

fog:x-->y-->z, or just fog:x-->z for short.

1-1 means we can "reverse the arrows" (because each y = g(x) came from a single x, and each z = f(y) came from a single y). so:

f^-1:z-->y g^-1:y-->x

now express a function that takes z-->x in 2 different ways: one as the inverse of fog, and another as some composition......