- What is Cartesian Sets
- |
- What is relations?
- |
- What is Function
- |
- Algebra of Real Function
- |
- Type Of Relations
- |
- Type Of Functions
- |
- Composite Function
- |
- Invertible Function

gof=g(f(x) for all x ∈ A

f(x) =(x+3)

g(x) =x

gof=g(f(x))=g(x+3)=(x+3)

Similarly

fog=f(g(x))=f(x

In this case

fog ≠ gof

such that

g(y)=x when y=f(x). It is denoted as f

fog=y gof=x

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

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

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