The inverse function of $$f(x)=82x-8-2x82x+8-2x$$,x∈$$(-1$$,$$1)$$, is

Correct option is 414log8eloge1+x1-x

Questions

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

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detailed solution

Correct option is D

y=82x-8-2x82x+8-2x⇒1+y1-y=82x8-2x⇒84x=1+y1-y⇒4x=log81+y1-y⇒x=14log81+y1-y∴f-1(x)=14log81+x1-x=14log8e loge1+x1-x

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The inverse function of f(x)=82x-8-2x82x+8-2x,x∈(-1,1), is

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