Continuity and intermediate value theorem

[saquibaa]

let [x,y] be in R and be a closed bounded interval and let g: [x,y] --> R be a function. suppose g is continuous. let k exist in R. suppose that k is strictly between g(x) and g(y) and that g-1(k) has at least 2 elements. prove that there is some m that is strictly between g(x) and g(y) and that g-1(m) has at least three elements.

i can't visualize this (i.e. with just 2 elements for g-1(k)). i know i need to use intermediate value theorem but can't come up with anything concrete.

 

[saquibaa]

please help...

 

[Office_Shredder]

i can't visualize this (i.e. with just 2 elements for g-1(k))

Start by drawing a picture. Pick where g(x) and g(y) are, and pick two points that have the same y-value in between x and y. Then start drawing a couple of graphs