Question

What’s is the inverse function of a(m)=0.6735e^0.423m

Answer 1

`a^(-1)(m)=(ln((m)/(0.6735)))/(0.423)`

Explanation:

The function is
`a(m)=0.6735e^(0.423m)`

Changing functional notation of a(m) to y:

`y=0.6735e^(0.423m)`

Now, interchanging m and y:

`m=0.6735e^(0.423y)\\`

Now, solving for y:

`e^(0.423y)=(m)/(0.6735)\\ln[e^(0.423y)]=ln[(m)/(0.6735)]\\0.423y=ln((m)/(0.6735))\\y=(ln((m)/(0.6735)))/(0.423)`

Thus, the inverse function is:

`a^(-1)(m)=(ln((m)/(0.6735)))/(0.423)`