The inverse of the function y=10x−10−x10x+10−x is

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log10(2−x)

12log101+x1−x

12log10(2x−1)

14log(2x2−x)

answer is B.

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Detailed Solution

Since, y=102x−1102×+1 ⇒ y102x+y=102x−1 ⇒ 102x=1+y1−y ∴ 2xlog1010=log101+y1−y ⇒ x=12log10(1+y1−y) Hence, the inverse of y is 12log10(1+y1−y) .

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