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

Answer 1

P(g(x))
= p(4-3x)
= 4 + 2√(4 - 3x + 2)
= 4 + 2√(6-3x)

remember we cannot take the square root of a negative, so
6-3x≥0
-3x ≥ -6
x ≤ 2

so the largest value of a is 2