Chapter 5 - Logarithmic, Exponential, and Other Transcendental Functions - 5.3 Exercises - Page 345: 77

600

To find the inverses, replace $f(x)$ by $x$ and $ x$ by $ f^{-1}(x)$ and solve for $ f^{-1}(x)$. Thus $ x = \frac{1}{8}f^{-1}(x)-3 ⇒f^{-1}(x)= 8(x+3)$ So, $(f^{-1} o f^{-1})(6) = f^{-1}(f^{-1}(6)) = f^{-1}(8(3+6)) = f^{-1}(72) =8(3+72) = 600 $