Question 14

Calculus Level 5

Let $f:[1,10]\to \mathbb Q$ be a continuous function then $\int_{f(2)}^{f(7)}\dfrac {f(x)}{f(x)+f(9-x)} dx$

$\bullet$ This question is part of the set For the JEE-nius;P

\dfrac {5}{2}

\dfrac {7}{3}

1 solution

Prakash Chandra Rai
Mar 23, 2015

Since f(x) is continuous function. Therefore f(7)= f(2). Because there are infinite irrationals between two consecutive rational numbers, hence only possible function is a constant function.

Only possible solution is f(x)= c where c is a constant. This implies that f(2) = f(7)

Seriously $310$ points for this problem.

Prakhar Gupta - 6 years, 2 months ago

Nice question for JEE but over rated

Ravi Dwivedi - 5 years, 5 months ago

@Prakash Chandra Rai Why is f(7)=f(2).........y=x^2 is continuous in [1,10] but f(2) is not equal to f(7)....

Aaghaz Mahajan - 3 years, 3 months ago

I agree with your point.

Sahil Silare - 3 years, 3 months ago

I know......IDK how he solved the problem.....any thoughts??

Aaghaz Mahajan - 3 years, 3 months ago

y=x^2 does not satisfy the given condition as range includes irrational numbers (eg- pi^2), thats why we cant consider it. Constant function however satisfies, f(x) = c where c is rational.

Natalia Dcruz - 3 years, 3 months ago

Question 14

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