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.
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"
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......