QJEEM22Ma3cd6: JEE Main 2022 Mathematics - Class 12 JEEM22Ma3cd6 Solution: Let f : R → R be defined as f ( x ) = x 3 + x − 5 . If g(x) is…

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QJEEM22Ma3cd6: JEE Main 2022 Mathematics - Class 12 JEEM22Ma3cd6 Solution: Let f : R → R be defined as f ( x ) = x 3 + x − 5 . If g(x) is…

Let f : R $\to$ R be defined as $f (x) = x^{3} + x - 5$ . If g(x) is a function such that $f (g (x)) = x, \forall^{'} x^{'} \in R$ , then g'(63) is equal to ________________.

Multiple Choice Options

A 149
B 349
C 4349
D 9149

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Accepted Answer

$f (x) = 3 x^{2} + 1$

f'(x) is bijective function

and $f (g (x)) = x \Rightarrow g (x)$ is inverse of f(x)

$g (f (x)) = x$

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

$g^{'} (f (x)) = \frac{1}{3 x^{2} + 1}$

Put x = 4 we get

$g^{'} (63) = \frac{1}{49}$

QJEEM22Ma3cd6: JEE Main 2022 Mathematics - Class 12 JEEM22Ma3cd6 Solution: Let f : R → R be defined as f ( x ) = x 3 + x − 5 . If g(x) is…

Multiple Choice Options

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