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

$fog$  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.