Published by:
CGP EDU Academic Team
Published on: August 14, 2026
Let f: R 
R and g: R 
R be functions satisfying
f(x + y) = f(x) + f(y) + f(x)f(y) and f(x) = xg(x) for all x, y 
R . If 
g(x) = 1, then which of the following statements is/are TRUE?
A
f is differentiable at every x 
R
R
B
If g(0) = 1, then g is differentiable at every x 
R
R
C
The derivative f (1) is equal to 1
D
The derivative f (0) is equal to 1
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
Also 
is continuous 
is differentiable and 
Also 
Now if 
is continuous at 
is diff. 
if 
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