For $e(g, d) = c $, can we compute $d$, given others

Question

Given $$e(g, d) = c $$ where,

• $e$ is bilinear pairing function chosen by the user/attacker,
• the values of $g$ and $c$ are known
• $g, d ∈ \mathbb{G}_1$ , $c$ depends upon the $e$

can we somehow compute the value of $d$

In a high level, I am asking if there exists a function $f$ that, in one way is the inverse of a $e$ can be used to compute $d$?