Question

Let \( f(x) = \dfrac{x-1}{x+1} \), \( f^{(1)}(x) = f(x) \), \( f^{(2)}(x) = f(f(x)) \), and \( g(x) + f^{(2)}(x) = 0 \). The area of the region enclosed by the curves \( y = g(x) \), \( y = 0 \), \( x = 4 \), and \( 2y = 2x - 3 \) is:

• A. \(\frac{1}{4} + \ln 2\)
• B. \(\frac{1}{8} + 2\ln 2\)
• C. \(\frac{1}{4} + 2\ln 2\)
• D. \(\frac{1}{8} + \ln 2\)

Answer 1

The Correct Option is D