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5Question: Let $ g(x^2 + 2) = x^4 + 4x^2 + 5 $. Find $ g(x^2 - 2) $.
g(x^2 + 2) = x^4 + 4x^2 + 5
We aim to find $ g(x^2 - 2) $.
Let’s define a substitution to help simplify. Let:
u = x^2 + 2 \Rightarrow x^2 = u - 2
x^4 = (x^2)^2 = (u - 2)^2 = u^2 - 4u + 4