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Please Solve RD Sharma Class 12 Chapter Function Exercise 2.4 Question 24 Subquestion (ii) Maths Textbook Solution.

Answers (1)


                fog  is a surjection.


                A\rightarrow A,g:A\rightarrow A

Onto function means each image has preimage in domain of f

A\rightarrow A,g:A\rightarrow A  are two bijections

Then,fog:A\rightarrow A

Onto condition:

Let z  be an element in the domain of  fog\left ( A \right )

Now, z\: \epsilon \: A(Codomain of  f) f is surjective.

So, z=f\left ( y \right ), where y\: \epsilon \: A                                                                                                                        … (i)

Now, y\: \epsilon \: A and g is a surjection

y=g\left ( x \right ), where x\: \epsilon \: A                                                                                                                             … (ii)

From (i) and (ii)

z=f\left ( y \right )=f\left ( g\left ( x \right ) \right )= \left ( fog \right )\left ( x \right ), where x\: \epsilon \: A

So, fog is a surjection.


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