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# Help function

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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