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Functions question

2025 · Shift 2 · Q30

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PYQ Library
JEE Advanced
Mathematics
Functions
2025 · Shift 2 · Q30

Functions question

2025 · Shift 2 · Q30

JEE AdvancedMathematicsFunctionsNumerical+4 / −1

Let

\mathbb{R}

denote the set of all real numbers. Let

f: \mathbb{R} \rightarrow \mathbb{R}

and

g: \mathbb{R} \rightarrow(0,4)

be functions defined by

f(x)=\log _e\left(x^2+2 x+4\right), \text { and } g(x)=\frac{4}{1+e^{-2 x}}

Define the composite function

f \circ g^{-1}

by

\left(f \circ g^{-1}\right)(x)=f\left(g^{-1}(x)\right)

, where

g^{-1}

is the inverse of the function

g

. Then the value of the derivative of the composite function

f \circ g^{-1}

at

x=2

is

\underline{\hspace{2cm}}

.

Numerical answer

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