I am asked to find an example of a discontinuous function f : [ 0 , 1 ] &#x

Dayami Rose

Dayami Rose

Answered question

2022-06-26

I am asked to find an example of a discontinuous function f : [ 0 , 1 ] R where the intermediate value theorem fails. I went over the intermediate value theorem today

Let f : [ a , b ] R be a continuous function. Suppose that there exists a y such that f ( a ) < y < f ( b ) or f ( a ) > y > f ( b ) . Then there exists a     c [ a , b ] such that f ( c ) = y.

I understand the theory behind it, however, we did not go over many example of how to use it to solve such problems so I do not really know where to begin

Answer & Explanation

grcalia1

grcalia1

Beginner2022-06-27Added 23 answers

Look for a function with a jump discontinuity.

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