Let fCR be a function where C is a closed and bounded interv

Let f:CR be a function where C is a closed and bounded interval and suppose that f is bounded. Then f is continuous.

True or False

Solution

False

Let C=[0,1]

Let

f(x)=x , 0<=x<0.5

f(x)=1+x, 0.5<=x<=1

f(x) is bounded and C is a closed and bounded interval but f(x) has a discontinuity at x=0.5.