I'm not sure what you are after. Is this helpful?
Plot[Sin[1/x], {x, .1, 10},
Axes -> False,
Frame -> True,
FrameTicks -> {{Automatic, Automatic}, {Automatic, Transpose[{#, 1/#}] &@DeleteCases[FindDivisions[{.1, 10}, 5], 0]}},
FrameLabel -> {{"f", ""}, {"1/t", "t"}},
BaseStyle -> 18]
