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Python 3, 61 60 59 bytes



lambda s,t="(/&lt;[{}]&gt;\)":[(c+t)[~t.find(c)]for c in s][::-1]


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 -1 byte thanks to @xnor. 

Changed the lookup string, so that the c in t test is eliminated.



Python 2, 63 bytes



lambda s,b='(/&lt;[{}]&gt;\)':map(dict(zip(b,b[::-1])).get,s,s)[::-1]


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-1 byte thanks to @xnor.

Python 3, 65 64 bytes



lambda s,b=b'(/&lt;[{}]&gt;\)':s.translate(dict(zip(b,b[::-1])))[::-1]


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Just for fun using idiomatic Python. (More idiomatic would be using str.maketrans, but it's way too long.)

-1 byte for both because the \ in '\)' doesn't need to be escaped.