Answer
$a=\pm3$
Work Step by Step
If $f\circ g$ crosses the y-axis at $23$ that means that $(f\circ g)(0)=23.$
$g(0)=3(0)+a=0$. Thus $(f\circ g)(0)=f(g(0))=f(a)=2a^2+5=23.$
Solve the above equation to obtain: $2a^2+5=23\\2a^2=18\\a^2=9\\a=\pm3$
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 - 5.1 Composite Functions - 5.1 Assess Your Understanding - Page 255: 55
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