Consider the function fx=tan^(-1)(3x-2)/(3+2x), ∀x≥0. If gx is the inverse function of fx, then the value of g^(′) (π)/4 is equal to

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MARKS Content Team · Accepted Answer

Correct answer: 26. fx=tan^(-1)(x-23)/(1+x.23)=tan^(-1)x-tan^(-1)2/3 ⇒f^(')x=1/(1+x^2) ... 1 Now, g^(')fx=1/(f^(')x) ∵ gfx=x} Putting x=5, we get, g^(')f5=1/(f^(')5)⇒g^(')tan^(−1)(35−2)/(3+25)=1/(11+5^2) ⇒g^(')tan^(−1)1=26⇒g^(')(π)/4=26

Consider the function $f (x) = t a n^{- 1} \{\frac{3 x - 2}{3 + 2 x}\}, \forall x \geq 0 .$ If $g (x)$ is the inverse function of $f (x),$ then the value of $g^{'} (\frac{π}{4})$ is equal to

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More Differentiation Questions

Consider the function fx=tan-13x-23+2x, ∀x≥0. If gx is the inverse function of fx, then the value of g ′ π 4 is equal to

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More Differentiation Questions

Consider the function $f (x) = t a n^{- 1} \{\frac{3 x - 2}{3 + 2 x}\}, \forall x \geq 0 .$ If $g (x)$ is the inverse function of $f (x),$ then the value of $g^{'} (\frac{π}{4})$ is equal to