Ch 2.6 - 88AE

Solution 88AE Step-1 A continuous function can be formally defined as a f unction f : x y ,where the preimage of every open set in y is open in x. More concretely, a function f(x) in a single variable x is said to be continuous at point x if, 0 1. If f(x 0 is defined, so that x 0 is in the domain of ‘ f’. 2. lim f(x) exists for x in the domain of f. x x0 3. lim f(x) = f( x ). x x0 0 Left continuous : lim f(x) = f(a) , then f(x) is called a left continuous at x=a. xa Right continuous : lim xa)+= f(a) , then f(x) is called a right continuous a