If P(x) = 4 + 2*sqrt(x + 2) and G(x) = 4 + 8x, then what is the largest constant a such that P(G(a)) is defined?
+600 $P(G(a))=P(4+8a)=4+2\sqrt{6+8a}$.
We must have $8a+6\ge 0\implies 8a\ge -6\implies a\ge -\frac{3}{4}$. The minimum value of $a$ is $-\frac{3}{4}$, the maximum is non-existent.
