Ch 2.6 - 91AE

STEP_BY_STEP SOLUTION 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 is in t0e domain of ‘ f’. 2. lim f(x) exists for x in the domain of f. x x 0 3. lx x(x) = f( x ). 0 0 Left continuous : lim fxa f(a) , then f(x) is called a left continuous at x=a. Right continuous : lim f(x) =+f(a) , then f(x) is called a right continuous at x=a. xa 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 Definition ; (com posite function): Let g be a functio n from a set A to a set B , and let f be a unction from B to a set C . Then the co mposition of functions f and g , denoted by fg , is the function from A to C that satis