Answer
See below
Work Step by Step
Evaluate $f(g(x))$: $$f_1(f_1(x))=f_1(x)=x$$
Evaluate $f(y)$: $$f_2(f_2(x))=f_2(-x)=-(-x)=x$$
Hence, the solution is $f_1(x)=x$. Another solution is $f_2(x)=-x$
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