Let f be a real valued function satisfying f(x) + f(x + 6) …

Maths Definite Integral and Area Under Curves General Single Correct MCQ

Published by: CGP EDU Academic Team

Published on: August 13, 2026

Let f be a real valued function satisfying

f(x) + f(x + 6) = f(x + 3) + f(x + 9). Then f(t) dt is

A linear function of x

An exponential function of x

A constant function

None of these

Text Solution

Verified by Experts

The correct answer is:

f(x) + f(x + 6) = f(x + 3) + f(x+9) …(1)

x = x + 3

f(x + 3) + f(x + 9) = f(x + 6) + f(x + 12)

from eq n (1)

f(x) + f(x + 6) – f(x + 9) + f(x + 9)

= f(x + 6) + f(x + 12)

f(x) = f(x + 12)

Let g(x) = f(t) dt

g'(x) =

g ' (x) = f(x + 12) – f(x) = 0

So g(x) is a constant function

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