KVPY SX SB Exam 05-Nov-2017 Question Paper

Question : 90 of 120

Marks: +1, -0

The number of continuous functions f:[0,1]→R that satisfy

Solution:

Given equation can be written as

-1/30∫↖{1}↙{0}({\f(x)}/2-x)^2dx-∫↖{1}↙{0}x^2dx

∫↖{1}↙{0}x^2dx1/3=∫↖{1}↙{0}({\f(x)}/2-x)^2dx

0=∫↖{1}↙{0}({\f(x)}/2-x)^2dx

So, no of continuous function is 1.

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