For every pair of continuous functions f, g : [0, 1] R suc…

Maths JEE - Advanced Previous Year Paper JEE-Advanced-2014-Paper-1 Single Correct MCQ

Published on: August 14, 2026

For every pair of continuous functions f, g : [0, 1] R such that max{f(x) : x [0, 1]} = max{g(x) : x [0, 1]}, the correct statement(s) is(are)

) 2 + 3f = (g(c)) 2 + 3g(c) for some c

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

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

[0, 1] ) 2 = (g(c)) 2 for some c

[0, 1]

Text Solution

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The correct answer is:

CHECK THE SOLUTION.

(a,d)Let f (x) and g (x) achieve their maximum value at x 1 and x 2 respectively

h (x) = f (x) - g (x)

h (x 1 ) = f (x 1 ) - g (x 1 ) 0

h (x 2 ) = f (x 2 ) - g (x 2 ) 0

h = 0 where c [0, 1] f = g .

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