 Hi, and welcome to the session. Today we will discuss the following question which says for what value of k is the following function continuous at x equal to 2, f of x equal to 2x plus 1 when x is less than 2, k when x is equal to 2, and 3x minus 1 when x is greater than 2. Before moving on to the solution, let's recall that a function f of x is continuous at x equal to a if limit x tends to a plus f of x is equal to limit x tends to a minus f of x is equal to f of a. This is the key idea for this question. Now let's move on to its solution. Here in the question we are given that the given function is continuous at x equal to 2. That means we have limit x tends to 2 plus f of x is equal to limit x tends to 2 minus f of x is equal to limit x tends to 2 minus f of x is equal to f of x. So first of all let us find out the left hand limit at x equal to 2 that is limit x tends to 2 minus f of x. Now as we are given that f of x is equal to 2x plus 1 when x is less than 2. So this will be equal to limit x tends to 2 minus 2x plus 1 and this will be equal to limit h tends to 0 2 into 2 minus h plus 1 that is limit h tends to 0 4 minus 2 x. And this will be equal to 5 minus 2 into 0 that is 5. Next let us find out the right hand limit at x equal to 0 and this will be equal to limit x tends to 2 plus f of x is equal to 0. Now it is given that f of x is equal to 3x minus 1 when x is greater than 2. So this will be equal to limit x tends to 2 plus 3x minus 1 that is limit h tends to 0 3 into 2 plus h minus 1 which will be equal to limit h tends to 0 6 plus 3h minus 1 and this will give us limit h tends to 0 5 plus 3h that is 5 plus 3 into 0 which is equal to 5. Also we are given that f of x is equal to k for x is equal to 2 so that means f of 2 is equal to k. Now we have limit x tends to 2 minus f of x is equal to limit x tends to 2 plus f of x is equal to f of 2. Now here limit x tends to 2 minus f of x is equal to 5 limit x tends to 2 plus f of x is equal to 5 and f of 2 is equal to k so that means k is equal to 5. Thus for k equal to 5 the given function is continuous at x equal to 2 and thus this is the required answer for this question. With this we finish this session. Hope you must have understood the question. Goodbye take care and have a nice day.