Answer
$f(\alpha x)=a^{\alpha x}=(a^x)^{\alpha}=(f(x))^{\alpha}$.
Work Step by Step
We know that $a^{\alpha x}=(a^x)^{\alpha}$
If $f(x)=a^x$, then substitute $\alpha x$ in to obtain: $f(\alpha x)=a^{\alpha x}=(a^x)^{\alpha}=(f(x))^{\alpha}$.
Precalculus (10th Edition)
by Sullivan, Michael
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 - Page 285: 127
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