Answer
$f(x-2)=-x^2+5x-9$
Work Step by Step
Plugging in $(x-2)$ to $x$ in $f(x)$ to obtain:
\begin{align*}
f(x-2)&=-(x-2)^2+(x-2)-3\\
&=-(x^2-4x+4)+x-2-3\\
&=-x^2+4x-4+x-5\\
&=-x^2+5x-9
\end{align*}
Precalculus (10th Edition)
by Sullivan, Michael
Published by
Pearson
ISBN 10:
0-32197-907-9
ISBN 13:
978-0-32197-907-0
Chapter 2 - Functions and Their Graphs - 2.2 The Graph of a Function - 2.2 Assess Your Understanding - Page 69: 52
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