2) The following statements are all false. Disprove each of them by finding a counterexample.

(a) If a function g is differentiable at a and a function f is not differentiable at g(a), then the function

f g cannot be differentiable at a.

(b) If a function g is not differentiable at a and a function f is differentiable at g(a), then the function

f g cannot be differentiable at a.

(c) If a function g is not differentiable at a and a function f is not differentiable at g(a), then the

function f g cannot be differentiable at a.