a. False - The point of symmetry on \( f^{-1}(x) \) is the reflection of the point of symmetry of \( f(x) \) over the line \( y = x \). Since the point of symmetry of \( f(x) \) is \((3, 6)\), the point of symmetry on \( f^{-1}(x) \) is \((6, 3)\).
b. True - The domain of f^{-1}(x) is the range of f(x) and since the range of f(x) covers all real numbers, the domain of f^{-1}(x) is ((- \infty, \infty)).
c. False - If f(x) is a one-to-one function, then its inverse, f^{-1}(x), is also a function. Since f(x) is given as a cubic function and it doesn't have repeated values, f^{-1}(x) is a function.
d. False - The range of f^{-1}(x) is the domain of f(x). Since f(x) is a cubic function with a minimum value of (6), the range of f^{-1}(x) is [6, \infty]
