Let be a continuous real-valued function on the unit circle {x R2 : |x| =1} such

Question:

Let be a continuous real-valued function on the unit circle {x € R2 : |x| =1} such that
f (0, 1) = g(1, 0) = 0 and g(- x )= - g(x).
Define f: R2→R by
F (x) = {|x| . g (x/|x| x ≠0,
0 x = 0.
(a) If x € R2 and h: R →R is defined by h (t) = f (tx) show that h is differentiable.
(b). show that f is not differentiable at (0, 0) unless g = 0.