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?
\(P(G(a)) = 4+ 2 \sqrt {4+8a+2} \) defined
\(4+8a+2\ge 0 \)
\(6\ge -8a\)
\(8a\ge -6\)
\(a \ge (-6 /8) = -(3/4) \)
P(G(a)) is defined iff \(a \ge (-3/4)\)
So a has no upper bound , only lower bound.
