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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?

Guest Jun 7, 2021

Bginner · Answer 1 · 2021-06-07T10:53:38

$P(G(a)) = 4+ 2 \sqrt {4+8a+2}$ 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.