Problem

f: \mathbb{R} \to \mathbb{R}

f(x)

is a differentiable bijective function, then which of the following may be true. a.

(f(x) - x)f''(x) < 0, \forall x \in \mathbb{R}

(f(x) - x)f''(x) > 0, \forall x \in \mathbb{R}

c. If

(f(x) - x)f''(x) > 0

, then

f(x) = f^{-1}(x)

has no solution d. If

(f(x) - x)f''(x) > 0

, then

f(x) = f^{-1}(x)

has atleast a real solution