- 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

Class 12 Maths Class 12 Physics

- Mathematics - Class XII (Set of 2 Volumes)
- NCERT Solutions: Mathematics 12th
- NCERT Exemplar Problems: Solutions Mathematics Class 12
- Together with Mathematics with Solutions Class-12
- CBSE 15 Sample Papers Mathematics for Class 12th
- 37 Years Chapterwise Solved Papers (2015-1979): IIT JEE - Mathematics
- New Pattern Mathematics for JEE (Main): Advanced
- Mathematics Errorless JEE Main JEE Advanced Vol. I & II 2015

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