If f(x) = (10ˣ − 10⁻ˣ) / (10ˣ + 10⁻ˣ), then f⁻¹(x) is equal to:

If f(x) = (10ˣ − 10⁻ˣ) / (10ˣ + 10⁻ˣ), then f⁻¹(x) is equal to:

• A. ½ log₁₀((1+x)/(1−x))
• B. ½ log₁₀((1−x)/(1+x))
• C. log₁₀((1+x)/(1−x))
• D. log₁₀(2x/(1−x))

Answer: A) ½ log₁₀((1+x)/(1−x))

Explanation: Let y = (10²ˣ − 1) / (10²ˣ + 1). Cross multiplying gives y(10²ˣ + 1) = 10²ˣ − 1. Solving for 10²ˣ gives 10²ˣ = (1+y)/(1−y). Converting to log: 2x = log₁₀((1+y)/(1−y)), so x = ½ log₁₀((1+y)/(1−y)).