Suppose that is twice differentiable satisfying (i) (0) = 1, (ii) '(x) > 0 for all x 0, and (iii) (x) < 0

Suppose that ƒ is twice differentiable satisfying (i) ƒ(0) = 1, (ii) ƒ'(x) > 0 for all x ≠ 0, and (iii) ƒ"(x) < 0 for x < 0 and ƒ"(x) > 0 for x > 0. Let g(x) = ƒ(x²).
(a) Sketch a possible graph of ƒ.
(b) Prove that g has no points of inflection and a unique local extreme value at x = 0. Sketch a possible graph of g.