One way to think about finding the inverse is to think of the function as a
machine, into which you put your input number, x, and out of which comes 2x + 3/5.
You are asking for the reverse process.
Going forward, you:
(a) multiplied the input by 2
(b) then added 3/5.
To reverse this (and recover the original number) you would:
(c) subtract 3/5
(d) then divide by 2.
As a formula, the inverse is then (y - 3/5)(1/2)
You should always check your proposed answer (and there are two orders to do this in):
2[ (y - 3/5)(1/2) ] + 3/5 = y - 3/5 + 3/5 = y
[ (2x + 3/5) - 3/5 ](1/2) = (2x + 3/5 - 3/5)(1/2) = (2x)(1/2) = x
It is good to 'make sense' out of the process, and to be able to check your
conclusions. Function machines, as one of the standard 'representations' can
help you do that.