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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?

 Jun 7, 2021
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\(P(G(a)) = 4+ 2 \sqrt {4+8a+2} \)          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.

 Jun 7, 2021

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