Ruby, 71 6767 65 bytes
->g{Math.methods.find{|h|g[0g[0.5]==Math.send(h_1,0.5)rescue p}||:acosh}
Try it online! (2 extra bytes because TIO doesn't support _1
syntax)
Non-competing but if Math
worked like CMath
(which it should), then this could be 57 bytes
->g{Math.methods.find{g[0.5]==Math.send(_1,0.5)rescue p}}
Try it online! (2 extra bytes because TIO doesn't support _1
syntax)