Exercise 5 Let f be a continuous function on R such that imL

Exercise 5. Let f be a continuous function on R such that im()L and lim f()- Prove that for any real c between L+ and L, there exists r R such that f(a)c. ntinuous function on R suoch

Solution

given that the function is continuous on real line

L⁺ and L^- are end values of function then every value lying in between L⁺ and L^- should be assigned to atleast one value of xas it is continuous

hence  there exists x R such that f(x) = c