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Mathematics - Differentiation Question with Solution | TestHub

MathematicsDifferentiationDerivative of function and its inverseHard2 minPYQ_2020

MathematicsHardsingle choice

Let $f$ and $g$ be differentiable functions on $R$ such that $f o g$ is the identity function. If for some $a, b \in R, g^{'} (a) = 5$ and $g (a) = b,$ then $f^{'} (b)$ is equal to:

Options:

Answer:

A

Solution:

$f (g (x)) = x$

$\Rightarrow f^{'} (g (x)) . g^{'} (x) = 1$

Put $x = a$

$\Rightarrow f^{'} (g (a)) g^{'} (a) = 1$

$\Rightarrow f^{'} (b) \times 5 = 1$

$\Rightarrow f^{'} (b) = \frac{1}{5}$

Stream:JEESubject:MathematicsTopic:DifferentiationSubtopic:Derivative of function and its inverse

⏱ 2mℹ️ Source: PYQ_2020

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