find the value of c that makes the function continuous.

Question

f(x)= 2x+9 for x≤3

         -4x+c for x>3

Answer 1

function 2x+9 is continuous at each point and function -4x+c is also continuous at each point for all real values of c .To make f(x) continuous we need to check the value only at the point where definition of the function changes i.e.  at x=3   2x+9 at 3 = 2*3+9 = 6+9 = 15

since the continuous function has LHL = RHL so  -4x+c tends 15 for a very small change .

To find c  we put -4x +c  = 15     

                         -4*3+c = 15

                         -12  +c = 15

                                 c  = 15 + 12

                                 c  = 27