Published by:
CGP EDU Academic Team
Published on: August 13, 2026
Suppose that f is a differentiable function with the property that f(x + y) = f(x) + f(y) + xy and 
f(h) = 3
where [ . ] represents greatest integer function, then
A
f is a linear function
B
2f(1) = 
C
f(x) = 3x + 
D
f ’ (1) = 4
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
(b,c,d)
Given f(x+y) = f(x) + f(y) + xy ........(1)
and 
= 3
f ′ (x) = 
= 
⇒ f(x) = 3x + 
+ c
in equation (1) put x=0=y ⇒ f(0) = 0
Therefor f(x) = 3x + 
──────────────────────────────────────────────────────────────────────────────────────────
Prepare Smarter with CGP Edu
Get practice questions, solutions, and test series in one place.
Write a Review
Share your experience with this question and solution.
Commentary
Send your comment, doubt, correction, or feedback to admin.
Similar Questions
Explore conceptually related problems
The function , where assumes its minimum value only at one point, if . Find .
2. If be two fixed positive integers such that for all real , then is a periodic function with …
3. The domain of the function , where the symbols have their usual meanings, is the set . Find nu…
If , then . Find .
, then is equal to . Find .
Let and be the roots of , then is equal to Find .