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

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

Answers (1)

Answer:

                fog  is a surjection.

Given:

                A\rightarrow A,g:A\rightarrow A

Hint:
Onto function means each image has preimage in domain of f
Solution:

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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