 Hello students, let's work out the following problem. It says discuss the continuity of the function fx at x is equal to 0 if fx is 2x minus 1, if x is less than 0, it is 2x plus 1 if x is greater than equal to 0. So we are given given function as 2x minus 1 if x is strictly less than 0 and it is 2x plus 1 if x is greater than equal to 0. That means at x is equal to 0 the function is 2x plus 1 right. So f of 0 the function at the point 0 is 2 into 0 plus 1 that is 1. Now we know that the function will be continuous at a point C if left-hand limit is equal to the right-hand limit at that point and it is equal to f of C. So here f of 0 is 1. Now we need to check whether the left-hand limit at 0 is 1 and the right-hand limit at 0 is 1 or not. So now we find the left-hand limit that is LHL that is limit x approaching to 0 from the left-hand side. Now since x approaching to 0 from the left-hand side that is when x is less than 0 then the function is 2x minus 1. So it is limit x approaching to 0 from the left-hand side of 2x minus 1. Now since it is approaching from the left-hand side will have limit x approaching to 0 of 2 into 0 minus H minus 1 and here limit also changes. Limit H approaching to 0 so this is equal to limit H approaching to 0 of minus 2H minus 1. So this is equal to minus 1 which is not equal to f of 0. Let's now check the right-hand limit that is limit x approaching to 0 from the right-hand side. Now since from the right-hand side x is positive so the function is 2x plus 1 and this is written as limit H approaching to 0 of 2 into 0 plus H plus 1. So this is equal to limit H approaching to 0 of 2H plus 1 which is equal to f of 0. So we have got that LHL is not equal to f of 0, but it is equal to RHL. So this implies function fx is discontinuous x is equal to 0. As we know that for a function to be continuous at the point C limit, left-hand limit at point C is equal to right-hand limit at the point C is equal to f of C. So we have got that fx is discontinuous at x is equal to 0. So this completes the question and the session. Bye for now. Take care. Have a good day.