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Let f:[0,oo)to[0,oo)a n dg:[0,oo)to[0,oo...

Let `f:[0,oo)to[0,oo)a n dg:[0,oo)to[0,oo)` be non-increasing and non-decreasing functions, respectively, and `h(x)=g(f(x))dot` If `fa n dg` are differentiable for all points in their respective domains and `h(0)=0,` then show `h(x)` is always, identically zero.

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