Answer:
This contradict of the chain rule.
Step-by-step explanation:
The given functions are
[tex]f(x)=x^2[/tex]
[tex]g(x)=|x|[/tex]
It is given that,
[tex](f\circ g)(x)=|x|^2=x^2[/tex]
[tex](g\circ f)(x)=|x^2|=x^2[/tex]
According to chin rule,
[tex](f\circ g)(c)=f(g(c))=f'(g(c)g'(c)[/tex]
It means, [tex](f\circ g)(c)[/tex] is differentiable if f(g(c)) and g(c) is differentiable at x=c.
Here g(x) is not differentiable at x=0 but both compositions are differentiable, which is a contradiction of the chain rule
