Chapter 6 - Logarithmic Functions - 6.5 Solving Exponential Equations - 6.5 Exercises - Page 528: 68

$f^{-1}(x) = \ln_ (\frac{x}{4.2})$

$f(x) = 4.2e^{x}$ Let $f(x) = y$ $y = 4.2e^{x}$ Swap the variables $x$ and $y$ and then solve for $y$ to find the inverse: $x = 4.2e^{y}$ $(e)^{y} = \frac{x}{4.2}$ $y = \ln (\frac{x}{4.2})$ $y = \ln_ (\frac{x}{4.2})$ $f^{-1}(x) = \ln_ (\frac{x}{4.2}).$