Answer
$a=\pm3$
Work Step by Step
$f(g(x))=f(3x+a)=2(3x+a)^2+5=2(9x^2+6ax+a^2)+5$
The fact that it crosses the y-axis at $23$ means that $f(g(0))=23$.
Hence here $2(9\cdot0^2+6a\cdot0+a^2)+5=23\\2a^2=18\\a^2=9\\a=\pm3$
College Algebra (10th Edition)
by Sullivan, Michael
Published by
Pearson
ISBN 10:
0321979478
ISBN 13:
978-0-32197-947-6
Chapter 6 - Section 6.1 - Composite Functions - 6.1 Assess Your Understanding - Page 409: 55
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