When a function is both one-one and on-to then the function can have an inverse. In other words, a function with A as domain and B as co-domain. If each member of A is associated with each member of B and no two members of B is associated with one member of A and no two members of A is associated with one member of B then the function is said to have an inverse.
The function y = 2x + 1 has its domain as well as range as R. The inverse function is x = (y - 1)/2. This function also has its range and domain as R. If a given function is not one-one on its domain, we can choose a subset of the domain on which it is one-one, and then define its inverse function. The trigonometric functions sine is not one-one but part of its domain from -π/2 to π/2 is one-one, hence we can define this subset of the domain and find the inverse of the function with domain -1 to 1. Similarly other functions can be determined.
The graph of a function and its inverse is symmetrical in the line y = x. |

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