A function f that maps the interval [a,b] to the real numbers R is continuous. If a value y lies between f(a) and f(b), then by the intermediate value theorem, there exists a c in [a,b] such that f(c) equals y.
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suppose f [a, b] -- R is continuous and f(b) y f(a). Prove tha.pdf
1. suppose f: [a, b] --> R is continuous and f(b) ? y ? f(a). Prove that there is a c that is an element
of [a, b] such that f(c) = y
Solution
as f is continuous, it must cover all the points within its range, and hence,there is a
c that is an element of [a, b] such that f(c) = y