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.