 Hello and how are you all today? My name is Priyanka and I shall be helping you with the question. It says suppose fx is equal to a plus bx when x is less than 1, 4 when x is equal to 1 and b minus ax when x is greater than 1. If limit x approaches to 1, fx is equal to f of 1. What are the possible values of a and b? So here we are given that limit x approaches to 1, fx is equal to f of 1 and we are given these three functions. So we are given fx equal to a plus bx when x is less than 1, fx equal to 4 when x is equal to 1 and fx equal to b minus ax when x is greater than 1. So we have therefore limit x approaches to 1 from left hand side, fx here when x is equal to 1 we have the value of function as 4 and here we will have limit x approaches to 1 from right hand side fx. Let us find out the value first. Now here this means that limit x approaches to 1 from left hand side function is a plus bx. Now let us take the value of x as 1 minus h so as x approaches to 0 h also approaches to sorry as h as x approaches to 1 h approaches to 0. So we have limit h approaches to 0 a plus bx that is 1 minus h so the answer is a plus b let this be the first equation. Here we have the value of fx as 4 let this be the second equation and here let us find it out. We have limit x approaches to 1 from right hand side v minus ax. Now let x is equal to 1 plus h so as x approaches to 1 h approaches to 0. So we have limit h approaches to 0 v minus a 1 plus h on using the limit we have v minus a and let this be the third equation. So now from the first, second and third equation we have a plus b equal to 4 and v minus a equal to 4. Now on adding these two we have and on rearranging we will have 2b equal to 8 that implies the value of b is equal to 4. Now since the value of b is 4 the value of a will be equal to right it will be equal to 0. So the answer to this question is a is equal to 0 and the value of b is obtained as 4. Right this ends the session hope you understood the whole concept well have a very nice day ahead.