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 at x=a. If , lim f(x) = f(a) = lim f(x) , then f(x) is called a continuous function at x=a. xa xa+ If , f(x) is not continuous at x =a means , it is discontinuous at x=a. Step-2 For any real number x the absolute value or modulus of x is denoted by x . | | | |= { x , if x 0...