capable (Can refer to physical capability as well as the the mental side of things. Also common part of compounds.)
Opposite (closest): unfähig
able ("-fähig" - as a second part of adjectives)
A quick, fun look at "fähig", a useful word as a stand alone but even more useful in compounds. Also: die Fähigkeit and a bad poem :).
fähig, die Fähigkeit, -fähig
The original idea of this root was:
It’s quite visible in offspring like the German fangen (to catch) or the Latin based “pact” which originally was a “fixed agreement”.
But there are quite a few surprises in this family.
Here’s an overview over most of the English family members: