The inverse function of f x = 8 2 x - 8 - 2 x 8 2 x + 8 - 2 x , x ∈ - 1 , 1 , is __________.

y = 8 2 x - 8 - 2 x 8 2 x + 8 - 2 x ⇒ 1 + y 1 - y = 8 2 x 8 - 2 x (Applying componendo-dividendo) ⇒ 8 4 x = 1 + y 1 - y ⇒ 4 x = l o g 8 1 + y 1 - y f - 1 x = 1 4 l o g 8 1 + x 1 - x s

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MathematicsFunctionsInverseMedium2 minPYQ_2020

MathematicsMediumsingle choice

The inverse function of $f (x) = \frac{8^{2 x} - 8^{- 2 x}}{8^{2 x} + 8^{- 2 x}}, x \in (- 1, 1),$ is __________.

Options:

Answer:

Solution:

$y = \frac{8^{2 x} - 8^{- 2 x}}{8^{2 x} + 8^{- 2 x}}$

$\Rightarrow \frac{1 + y}{1 - y} = \frac{8^{2 x}}{8^{- 2 x}}$ (Applying componendo-dividendo)

$\Rightarrow 8^{4 x} = \frac{1 + y}{1 - y}$

$\Rightarrow 4 x = l o g_{8} (\frac{1 + y}{1 - y})$

$f^{- 1} (x) = \frac{1}{4} l o g_{8} (\frac{1 + x}{1 - x}) s$

Stream:JEESubject:MathematicsTopic:FunctionsSubtopic:Inverse

⏱ 2mℹ️ Source: PYQ_2020

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