Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 5 - Exponential and Logarithmic Functions - 5.3 Exponential Functions - 5.3 Assess Your Understanding: 125

Answer

\begin{align*} f(A+B)&=a^{A+B}=a^A\cdot a^B=f(A)\cdot f(B) \end{align*}

Work Step by Step

If $f(x)=a^x$, then: $f(A)=a^A\text{ and } f(B)=a^B$ Substitute $A+B$ to $x$ to obtain: \begin{align*} f(A+B)&=a^{A+B}\\ &=a^A\cdot a^B\\ &=f(A)\cdot f(B) \end{align*}
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