Let f : R R be defined as f ( x ) = ( 2 x - 3 ) 3 + 4 x 3 + cos x and g = f - 1 then the value of 7 g ' ( 2) + 3 g ' ' ( 2) (where g ' and g ' ' represent the 1 st and 2 nd order derivatives of g ) is

Question

Let $f : R \to R$ be defined as $f (x) = {(2 x - 3 π)}^{3} + \frac{4 x}{3} + \cos x$ and $g = f^{- 1}$ then the value of $7 g' (2 π) + 3 g'' (2 π)$ (where $g'$ and $g''$ represent the $1^{st}$ and $2^{nd}$ order derivatives of $g$ ) is _______

Smart Achievers · Accepted Answer

(3)

$g' (2 π) = \frac{3}{7}, g'' (2 π) = 0$

Solution

Q.
Let $f : R \to R$ be defined as $f (x) = {(2 x - 3 π)}^{3} + \frac{4 x}{3} + \cos x$ and $g = f^{- 1}$ then the value of $7 g' (2 π) + 3 g'' (2 π)$ (where $g'$ and $g''$ represent the $1^{st}$ and $2^{nd}$ order derivatives of $g$ ) is _______

Ans.
(3)

$g' (2 π) = \frac{3}{7}, g'' (2 π) = 0$

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Solution

Q. Let f:R→R be defined as f(x)=(2x-3π)3+4x3+cosx and g=f-1 then the value of 7g'(2π)+3g''(2π) (where g' and g'' represent the 1st and 2nd order derivatives of g) is _______

Ans. (3) g'(2π)=37, g''(2π)=0

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Q.
Let $f : R \to R$ be defined as $f (x) = {(2 x - 3 π)}^{3} + \frac{4 x}{3} + \cos x$ and $g = f^{- 1}$ then the value of $7 g' (2 π) + 3 g'' (2 π)$ (where $g'$ and $g''$ represent the $1^{st}$ and $2^{nd}$ order derivatives of $g$ ) is _______

Ans.
(3)

$g' (2 π) = \frac{3}{7}, g'' (2 π) = 0$