Answer
See below.
Work Step by Step
$f(g(x))=f(\frac{2}{x-3})=(\frac{2}{x-3})^2+2$
The denominator of the fraction cannot be $0$, thus the domain is all real numbers apart from $x=3$.
$f(g(5))=(\frac{2}{5-3})^2+2=(\frac{2}{2})^2+2=1^2+2=3$
College Algebra (10th Edition)
by Sullivan, Michael
Published by
Pearson
ISBN 10:
0321979478
ISBN 13:
978-0-32197-947-6
Chapter 6 - Cumulative Review - Page 503: 9
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