JEE PYQ: Differentiation Question 11
Question 11 - 2020 (09 Jan Shift 2)
Let $f$ and $g$ be differentiable functions on $\mathbb{R}$ such that $f \circ g$ is the identity function. If for some $a, b \in \mathbb{R}$, $g’(a) = 5$ and $g(a) = b$, then $f’(b)$ is equal to:
(1) $\frac{1}{5}$ (2) $1$ (3) $5$ (4) $\frac{2}{5}$
Show Answer
Answer: (1) $\frac{1}{5}$
Solution
$f’(g(x)) \cdot g’(x) = 1$. At $x = a$: $f’(b) \cdot 5 = 1$, so $f’(b) = \frac{1}{5}$.
BETA
