 Hi, and welcome to the session. Let us discuss the following question. Question phase, let function f from set 1, 3, 4 to set 1, 2, 5. And function g from set 1, 2, 5 to set 1, 3 be given by f is equal to set of ordered pairs of 1, 2, 3, 5, 4, 1. And g is equal to set of ordered pairs of 1, 3, 2, 3, 5, 1. Write down g os. First of all, let us understand if we are given a function f from a to b. And there is another function g from b to c. Then the composition of f and g is defined by g os, which is a function from a to c. We can see the codomain of function f is equal to the domain of function g. So we have defined the composition of f and g as g os. And it is a function from a to c. g os is a function given by g os equal to g fx for some x belonging to a. So clearly we can see g os is equal to g fx for every x belonging to set a. This is the key idea to solve the given question. Let us now start the solution. We are given function f from set 1, 3, 4 to set 1, 2, 5, which is given by set of ordered pairs of 1, 2, 3, 5, 4, 1. Now we are given another function g from set 1, 2, 5 to set 1, 3. It is given by g is equal to set of ordered pairs of 1, 3, 2, 3, 5, 1. Now clearly we can see f1 is equal to 2, f3 is equal to 5, f4 is equal to 1. We can write f1 is equal to 2, f3 is equal to 5, f4 is equal to 1. Now again g1 is equal to 3, g2 is equal to 3, g5 is equal to 1. So we can write g1 is equal to 3, g2 is equal to 3, g5 is equal to. Clearly we can see codomain of function f is same as domain of function g. So we can define composition of f and g as g os. g os is a function from set 1, 3, 4 to set 1, 3. So we can write g os is a function from 1, 3, 4 to set 1, 3 such that g of f1 is equal to gf1. Now we know f1 is equal to 2. So we will write it is equal to g of 2. Now we know g of 2 is equal to 3. So this is further equal to 3. We can write g of f1 is equal to 3. Now let us find out g of f3. g of f3 is equal to gf3. Now we know f3 is equal to 5. So we will write it equal to g5. So it is substituting for f3 we get g5. Now g of 5 is equal to 1. So we get g of f3 is equal to 1. Now we will find g of f4. We can write g of f4 is equal to gf4. Now we know f4 is equal to 1. So it is equal to g of 1. Now g of 1 is equal to 3. So we get g of f4 is equal to 3. Remember that 1, 3, and 4 belong to this set, which makes the domain of the function g of f. So now we can clearly see g of f is a function from set 1, 3, 4 to set 1, 3. And it is given by g of f equal to set of ordered pairs of 1, 3, 3, 1, 4, 3. So we can write it is equal to set of ordered pairs of 1, 3, 3, 1, 4, 1. This is the required answer. Hope you understood the session. Take care and goodbye.