Trying to summarize what I get here as a pattern: If \\(f\dashv g\\), then:

the right adjoint \\(g\\) approximates the inverse of \\(f\\) from above: \\(p\leq g(f(p))\\)

and

the left adjoint \\(f\\) approximates the inverse of \\(g\\) from below \\(f(g(q))\leq q\\).

[Edited: I switched "right" and "left" in my first attempt, as Valter points out below. ]

the right adjoint \\(g\\) approximates the inverse of \\(f\\) from above: \\(p\leq g(f(p))\\)

and

the left adjoint \\(f\\) approximates the inverse of \\(g\\) from below \\(f(g(q))\leq q\\).

[Edited: I switched "right" and "left" in my first attempt, as Valter points out below. ]