Find value of c that makes function continuous

Question

f(x) = [ c(x-1)] / (|x-1|) ; x<1 

          c+cos(1-x)-1 ; x geater/equal to 1 

 

 

I am very confused. This whole thing looks really complicated.

Answer 1

If x<1, x-1<0.  So, lx-1l = -(x-1)

 

When x < 1, f(x) = [c(x-1)]/lx-1l = c(x-1)/[-(x-1)] = -c

 

The function will be continuous when x = 1 if and only if the two pieces of the graph of f(x) fit together when x = 1.

 

So, we must have -c = c+(cos(1-1))-1

 

                          -c = c + 1 - 1

 

                         -2c = 0

 

                            c = 0