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For every pair of continuous functions f...

For every pair of continuous functions `f,g:[0,1]->R` such that `max{f(x):x in [0,1]}= max{g(x):x in[0,1]}` then which are the correct statements

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f,g are continuous functions
`max{f(x):x in[0,1]}=max{g(x):x in[0,1]}`
graphs of both function will intersect at one point given`x in [0,1]`
Let that point be C.
f(C)=g(C)
A)`[f(c)]^2+3f(c)=g(c)^2+3g(c)`
`[f(c)]^2-g(c)]^2+3f(c)-3g(c)`
`[f(c)-g(c)][f(c)+g(c)]+3[f(c)-g(c)]`
...
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