I need a practical example of inverse functions and their use.

A practical example of an inverse function could be the
following. A particle travels at a varying speed which is given by v(t) = 3t + 6, where
t is the time travelled by the particle.

Now if we denote
v(t) = v = 3t +6

=> 3t = v -
6

=> t = (v -
6)/3

Denote t by
v^-1(t).

=> v^-1(t) = (v -
6)/3

v^-1(t) is the inverse function of
v(t).

v^-1(t) here is the time and it is given in terms of
the speed v.

The function v(t) = 3t + 6 gives the speed of
the particle in terms of the time t it has been travelling. v^-1(t) = (v - 6)/3 gives
the time that the particle has been travelling if we know its velocity
v.