Prove that if is differentiable on (-, ) and '(x) < 1 for all real numbers, then has at most one fixed point.

Prove that if ƒ is differentiable on (-∞, ∞) and
ƒ'(x) < 1 for all real numbers, then ƒ has at most one fixed
point. A fixed point of a function ƒ is a real number c such that
ƒ(c) = c.