Beyond the Basics

111.
1. $f (x) + g (x) = 2 \cdot 3^{x}$ $f (x) + g (x) = 2 \cdot 3^{x}$
2. $f (x) - g (x) = 2 \cdot 3^{- x}$ $f (x) - g (x) = 2 \cdot 3^{- x}$
3. ${[f (x)]}^{2} - {[g (x)]}^{2} = 4$ ${[f (x)]}^{2} - {[g (x)]}^{2} = 4$
4. ${[f (x)]}^{2} + {[g (x)]}^{2} = 2 (3^{2 x} + 3^{- 2 x})$ ${[f (x)]}^{2} + {[g (x)]}^{2} = 2 (3^{2 x} + 3^{- 2 x})$
115. $y = e^{x} \to y = e^{x - 1} \to y = e^{2 x - 1} \to y = 3 e^{2 x - 1}$ $y = e^{x} \to y = e^{x - 1} \to y = e^{2 x - 1} \to y = 3 e^{2 x - 1}$
117. $y = e^{x} \to y = e^{2 + x} \to y = e^{2 + 3 x} \to y = 5 e^{2 + 3 x} \to y = 5 e^{2 - 3 x} \to y = 5 e^{2 - 3 x} + 4$ $y = e^{x} \to y = e^{2 + x} \to y = e^{2 + 3 x} \to y = 5 e^{2 + 3 x} \to y = 5 e^{2 - 3 x} \to y = 5 e^{2 - 3 x} + 4$

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