 Hello and welcome to the session. In this session, a function f is defined as f of x is equal to minus x when x is less than 0, x plus 5 when 0 is less than x, less than 1, and minus 1 when x is greater than equal to 1. The e-part is, find the domain of the function f and b-part for 3 by 4. Now before starting the solution of this question, we should know what is the function f, the function f is equal to, which belongs to the set of real numbers defined as a key idea for solving out this question. And now we'll start with the solution given that the function is equal to when x is less than 0, less than x, less than 1, when x is greater than equal to 1. Now this function is defined when x is less than 0, x is less than between 0 and 1, and x is greater than equal to 1. This is not defined when x is equal to 0. Now using this result, which is given in the key idea, the domain, because for all values of x is equal to x is equal to 2 into f of x, now the function f is defined as this, x is equal to minus x when x is less than 0. Now here, 0 x will be equal to 2 into when x is less than 0, that is equal to minus x when 0 is less than x, less than 1. It will be equal to 2 into plus 5 minus 4 x when 0 is less than x, less than x is equal to x plus 5 when 0 is less than x, less than 1. Now f of x is equal to x is equal to minus 1 when x is greater than equal to 1. So gfx will be equal to 2 into x is equal to minus 1 minus 4 x when minus 2 x minus 4 x when x is less than x, less than 1 minus 4 x when x is greater than equal to 0. So gfx is equal to minus 6 x when x is less than 0, 0 is less than x, is less than 1, is 4 x when x is second sub part. But we have to find 2 into f of minus 6 plus 3 into f of 2 plus 3 by 4. We have to find f of minus 6. Now here that means x is less than 0 is equal to minus x when f of x is equal to minus x. f of minus 6 is equal to minus of minus 6 which is equal to 6, f of 2. Now here x is equal to 2, when equal to 1 then minus 1 which is equal to 1 by 2. Now we will find f of 3 by 4. Now here x that means x is lying between 0 and 1. x is equal to x plus 5 when 0 is less than x, less than 1. Therefore when less than 1 then f of x is equal to x plus 5 is equal to 3 by 4 is equal to 3 plus 24 which is equal to 23 by 4. Now this is the value of f of minus 6 of 3 by 4. So what will happen? This will be into 1 by 2 plus which is equal to 12 plus 23 by 4 which is 48. So this is the solution of the given question and that's all for this session. Hope you all have enjoyed the session.