 In this video we present the solution to question number five for practice exam number two for math 12-10 in which case we're asked to find the value of c that makes the function the piecewise function f of x continuous where f is given as the first part is two minus x quantity squared where x is less than or equal to four and then the second part is the square root of c minus two x when x is greater than four. Because our functions piecewise and the pieces themselves are continuous pieces the first piece is just a polynomial function which is continuous the second piece is just a radical function which is continuous. Our function is going to be a piecewise continuous function that is it's built with continuous pieces so the only place where we might have a discontinuity which will necessarily be a jump discontinuity will be at the switching number of x equals four so we need to make sure the left side of x equals four agrees with the right side of x equals four. So what happens when we're a little bit to the left of x equals four we're going to get that the limit as x approaches four from the left of f of x here this is just going to look like our function two minus x quantity squared as x approaches four from the left in which case because it's continuous we can plug in x equals four to get two minus four squared we end up with two negative two squared and we end up with a positive four so the left side the left limit is going to be positive four we need to make sure that the right limit is also four as x approaches four from the right of f of x well this time we're going to get that as we approach four from the right it's going to look like the square root function like so we get the square root of c minus two x for which again because this branch is continuous we plug in four to get the evaluation we get the square root of c minus two times four so we get the square root of c time our c minus eight so in order to be continuous these two pieces the left limit the right limit have to agree with each other so we have to solve the equation the square root of c minus eight is equal to four to do that we're going to square both sides we get c minus eight is equal to 16 then we're going to add eight to both sides and we get c equals 24 and so c equals 24 is the only parameter that will make this piecewise function continuous so the answer turns out to be d