The inverse of the function $$f(x)=ax$$−a−$$xax+a$$−x is

Correct option is 212loga⁡1+x1−x

Questions

The inverse of the function $f (x) = \frac{a^{x} - a^{- x}}{a^{x} + a^{- x}} is$

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12loga⁡1−x1+x

12loga⁡1+x1−x

loga⁡1+x1−x

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detailed solution

Correct option is B

Let y=ax−a−xax+a−x=a2x−1a2x+1 ⇒y−1y+1=a2x−1−a2x+1a2x−1+a2x+1(Using componendo and dividendo)⇒y−1y+1=−22a2x⇒a2x=1+y1−y⇒2xloga⁡a=loga⁡1+y1−y⇒x=12loga⁡1+y1−y

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The inverse of the function f(x)=ax−a−xax+a−x is

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The inverse of the function $f (x) = \frac{a^{x} - a^{- x}}{a^{x} + a^{- x}} is$