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Here's the way we can test for an inverse.....put first function into the second....then, put the second function into the first.....if we get an "x" as a result in both cases....they are inverses

First one

(x - 6) + 6   =   x

(x + 6) - 6  =   x         these are inverses

Second one

2  [ ( x + 7) / 2 ] - 7   =    x + 7 - 7   =  x

 ( [ 2x - 7 ] + 7 )  / 2  =      [2x] / 2   =  x             these are inverses

The inverse just reverses the coordinates...so we have

(-3, 1), ( 3 , -2), (1, 5) , (4, 6)

We don't have any single "x"  associated with two different "y's".....so.....the inverse is a function

(7, -5), ( -8, -6) , ( -2, 1), ( 3, 10 )

Again...no single x is  associated with two different "y's"....so....the inverse relation is a function