Given function is,
[tex] 4e^{f(x)^{-1}} =x-2 [/tex]
We need to find [tex] f(x)^{-1} [/tex]. So, we need to isolate [tex] f(x)^{-1} . [/tex]
Hence, the first step is to remove 4 from the left side. So, multiply each sides by 4. Therefore,
[tex] \frac{4e^{f(x)^{-1}}}{4} =\frac{x-2}{4} [/tex]
[tex] e^{f(x)^{-1}} = \frac{x-2}{4} [/tex]
Next step is to take natural log ln to each sides of the equation to get rid of f(x)^-1 from the exponent. So,
[tex] n e^{f(x)^{-1}} = ln \frac{x-2}{4} [/tex] Since [tex] ln e^x = x [/tex]
[tex] {f(x)^{-1}} = ln \frac{x-2}{4} [/tex]
So, [tex] {f(x)^{-1}} = ln \frac{x-2}{4} [/tex]
