2580.22 – If . . . Then . . .

If $f(x) = 4^x$ , then $f(x+1) - f(x) = \cdots$ .

(a) $4$ , (b) $f(x)$ , (c) $2 f(x)$ , (d) $3 f(x)$ , (e) $4 f(x)$ .

Solution

\begin{aligned} f(x+1) - f(x) &=& 4^{x+1} - 4^x \\ &=& 4 \cdot 4^x - 4^x \\ &=& (4 - 1) 4^x \\ &=& 3 \cdot 4^x \\ &=& 3 f(x) \end{aligned}