The function  is continuous on .

Consider .

If  for , then .

Here, .

From the above property, .

If  and , then .

From the above property,

.

Here .

If  , then .

Hence, .

Hence the property is verified.

(b)

.

Consider .

Here  is continuous on .

.

Since , then

Therefore,

.

(a) .

(b) .