Chapter 4 - Calculating the Derivative - 4.3 The Chain Rule - 4.3 Exercises - Page 226: 59

$P[f(a)]=18a^{2}+24a+9$

To find the composite function P[f(a)], $\bf{\text{ replace x with f(a)}}$ in the definition of P(x) \begin{align*} P[f(a)]& =2[f(a)]^{2}+1\quad & \\ &=2(3a+2)^{2}+1 \quad & \\ &=2(9a^{2}+12a+4)+1 \quad & \\ & =18a^{2}+24a+8+1\quad & \\ & =18a^{2}+24a+9 \end{align*}