Question

For the function \(f: [1, \infty) \rightarrow [1, \infty)\) defined by \(f(x) = (x - 1)^4 + 1\), among the two statements:
(I) The set \(S = \{x \in [1, \infty) : f(x) = f^{-1}(x)\}\) contains exactly two elements, and
(II) The set \(S = \{x \in [1, \infty) : f(x) = f^{-1}(x + 1)\}\) is an empty set,
Options:

• A. only (I) is TRUE
• B. only (II) is TRUE
• C. both (I) and (II) are TRUE
• D. neither (I) nor (II) is TRUE

Answer 1

The Correct Option is A