Problem

The key is recognizing that function composition often simplifies dramatically—especially when the function has a special structure. Calculate $f(f(x))$ and $f(f(1/x))$ explicitly, then look for how they combine. You'll likely find that $y$ reduces to a much simpler expression in $x$, and then finding its minimum becomes a straightforward calculus or inequality problem. The symmetry in the problem setup suggests the answer might be elegant.

The key is recognizing that function composition often simplifies dramatically—especially when the function has a special structure. Calculate $f(f(x))$ and $f(f(1/x))$ explicitly, then look for how they combine. You'll likely find that $y$ reduces to a much simpler expression in $x$, and then finding its minimum becomes a straightforward calculus or inequality problem. The symmetry in the problem setup suggests the answer might be elegant.