Let f be a function defined on an interval I = [a, b]. A continuous function on I is a function whose graph y = f(x) can be described by the motion of a particle travelling along it from the point (a, f(a)) to the point (b, f(b)) without moving off the curve.
If the left hand limit, right hand limit and the value of the function at x = c exist and equal to each other, then f is said to be continuous at x = c.
A function f is said to be continuous in an interval [a, b] if it is continuous at each and every point of the interval.
A function f is said to be discontinuous at a point c of its domain if it is not continuous at c. The point c is then called a point of discontinuity of the function.
If f and g be two real functions continuous at a real number c. Then
If f and g are real valued functions such that (fog) is defined at c. If g is continuous at c and if f is continuous at g(c), then (fog) is continuous at c.