Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 4 - Exponential and Logarithmic Functions - Section 4.1 Composite Functions - 4.1 Assess Your Understanding - Page 280: 63


$a=-3, 3$

Work Step by Step

We have: $f(x)=2x^2+5$ and $g(x)=3x+a$ $(f \circ g)$ crosses the y-axis at 23. This implies that $(f \circ g)(0)=23$ Now, $g(0)=(3)(0)+a =a$ So, $(f\circ g) (0) =f[g(0)]=f(a)=2a^2+5=23$ The above equation can be simplified as: $2a^2 +5 =23 \\ 2a^2=18 \\ a=\pm 3=-3, 3$
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