Let f: R → R satisfy the equation f(x + y) = f(x). f(y) for all x, y R and f(x) ≠ 0 for any x R. If the function f is differentiable at x = 0 and f'(0) = 3, then lim h → 0 1/h(f(h) - 1) is equal to _ _ _ _ _ _.

Limit, Continuity and Differentiability: JEE Main 2021 Mathematics question

JEE Main 2021 · 18 Mar, Evening shift · Q40

JEE Main 202118 Mar, Evening shiftMathematicsMediumLimit, Continuity and Differentiability420× since 2002

Let f : R

\to

R satisfy the equation f(x + y) = f(x) . f(y) for all x, y

\in

R and f(x)

\ne

0 for any x

\in

R. If the function f is differentiable at x = 0 and f'(0) = 3, then

\mathop {\lim }\limits_{h \to 0} {1 \over h}(f(h) - 1)

is equal to ____________.

Your answerType your answer. Integers and decimals are accepted.

JEE Main 2021 Limit, Continuity and Differentiability Question with Answer (18 Mar Evening shift, Q40) | JEE Arc