Let . If g(x) is inverse of function f(x), then the value of is

JEE MainMathematicsEasyITF

Let
$f(x) = x^{105} + x^{53} + x^{27} + x^{13} + x^{3} + 3x + 1$ . If g(x) is
inverse of function f(x), then the value of $9g^{'}(1)$ is

Show answer and solution

since g(x) is inverse of f(x)

g(f(x)) = x

Differentiating w.r.t. x

g^{'}(f(x)) \cdot f^{'}(x) = 1

x = 0,f(0) = 1

\therefore g^{'}(f(0)) \cdot f^{'}(0) = 1

g^{'}(1) = \frac{1}{f^{'}(0)}

\begin{matrix} \therefore f^{'}(0) = 3) & \therefore & g^{'}(1) = \frac{1}{3} \end{matrix}

Source: Grass-G / M-17 Mathematics Paper 26 Nov Second.docx

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