help in continuity?

Question

can ne one tell in detail what is
intermediate value property of continuos function

Answer 1

Basically the intermediate value property of continuous functions says that, if you know the value of a function at two points, then you know that between those two points, the function will have a maximum, a minimum, and will have at least one corresponding x-value for each y-value.

That sounds a lot more complicated than it is, so here's an example of how it's useful.

If you know f(0) = -5 and f(1) = 10 and that f is continuous, then you can say for certain that the graph of f crosses the x-axis at some point between 0 and 1, and that therefore f has a root between 0 and 1.

Answer 2

The Intermediate Value Theorem: If a function f is continuous on a closed interval [a,b] and if f(a) is not equal to f(b), then f takes on every value between f(a) and f(b) in the interval [a,b].

So, if w is any number between f(a) and f(b) (w is in the range), then there is a number c between a & b (c is in the domain) such that f(c) = w.