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If P(x) = 4+2*sqrt(x + 3) and G(x) = 4-8x, then what is the largest constant a such that P(G(a)) is defined?

 Feb 7, 2022
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Since P(G(a)) has to be defined, the term under the square root has to be greater than or equal to 0. This means that (4-8x)+3 >= 0. This simplifies to 7 >= 8x, which further simplifies to x <= 7/8. This means that the largest possible value of x is 7/8.

 

Let me know if I did anything wrong!

 Feb 7, 2022

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