Inverse Mapping of A Mapping
If f is a mapping from a set A to a set B, then the set A is called the domain and the set B is called the co-domain of the mapping f.
Let f : A → B be bijective i.e., both one-to-one and onto. Then the mapping g : B → A is called the inverse mapping of the mapping f if
f (x) = y
g(y) = x where, xA , yB
The inverse mapping of the mappinf f is usually represented by f-1.
Only one-to-one onto mappings posses inverse mapping.
From the defition of inverse mapping it is obvious that if f(x) = y, then f-1(y) = x, and vice-versa.
Inverse Circular Functions and Their Principle and General Values
Inverse circular functions are defined as follows:
If sin θ=x, then or arc sin x.
If cos θ=x, then or arc cos x,
If tan θ=x, then or arc tan x,
and similar definitions for other trigonometric functions.
Thus if then sin-1 x represents an angle whose sine is x.