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Find the inverse function of f(x) = (2/3) · (10^x - 10^-x)/(10^x + 10^-x).

1. (1/3) log10((1 + x)/(1 - x))
2. (1/2) log10((2 + 3x)/(2 - 3x))
3. (1/3) log10((2 + 3x)/(2 - 3x))
4. (1/6) log10((2 - 3x)/(2 + 3x))

Correct answer: (1/2) log10((2 + 3x)/(2 - 3x))

Solution

The correct option is right because it accurately represents the inverse of the given function, which involves manipulating the original function's expression to isolate x and express it in terms of y, leading to the logarithmic form that matches the structure of option B.

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