## Invertible Function:

If the Function f : A-> B is both one to one and onto i.e bijective ,then we can find a function g: B-> A

such that

g(y)=x when y=f(x). The function g is called the inverse of f and is denoted as f

^{-1}. The function f(x) is called invertible function

**Another definition of Invertible function**
A Function f : A-> B is invertible if we can find a function g: B- > A such that

fog=y gof=x

**Example**
A set A is defined as A={a,b,c}

Let f: A-> A be the function defined as are

(1) f={(a,a),(b,b),(c,c)}

(2) f={(a,b),(b,a),(c,c)}

(3) f={(a,c),(b,c),(c,a)}

Find if all these function defined are invertible

**Solutions**
(1) The neccesary condition for invertibleness is one on one and onto

This function is clearly one on one and onto,so it is invertible

(2) This function is clearly one on one and onto,so it is invertible

(3) This function is not one on one and neither onto,so it is not invertible

## Related Topics

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Class 12 Maths
Class 12 Physics