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For every pair of continuous function f,...

For every pair of continuous function `f, g : [0, 1] rarr R` such that max `{f(x) : x in [0, 1]} = max {g(x) : x in [0, 1]}`. The correct statement(s) is (are)

A

`[f(c)]^(2) + 3f(c) = [g(c)]^(2) + 3 g(c)"for some c" in [0, 1]1`

B

`[f(c)]^(2) + f(c) = [g(c)]^(2) + 3g(c)"for some c" in [0, 1]`

C

`[f(c)]^(2) + 3f(c) = [g(c)]^(2) + g(c)"for some c" in [0, 1]`

D

`[f(c)]^(2) = [g(c)]^(2)"for some c" in [0, 1]`

Text Solution

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The correct Answer is:
A, D
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