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 \lim_{x\to0} g(x) = 1,then which of the following statements is/are TRUE? [JEE Adv 2020 P2]

f is differentiable at every x ∈ R

If g(0) = 1, then g is differentiable at every x ∈ R

The derivative f'(1) is equal to 1

The derivative f'(0) is equal to 1

Limits, Continuity and Differentiability

Section: Mathematics

Question : 14 of 51

Marks: +1, -0

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

lim

x→0

g(x) = 1,then which of the following statements is/are TRUE?

[JEE Adv 2020 P2]

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