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📅 May 14, 2026 👤 scraface

May 14, 2026

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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
Substituting into the expression for $ g(u) $:
g(u) = x^4 + 4x^2 + 5 = (u^2 - 4u + 4) + 4(u - 2) + 5
g(u) = u^2 - 4u + 4 + 4u - 8 + 5 = u^2 + 1
So, $ g(u) = u^2 + 1 $.
Now substitute $ u = x^2 - 2 $:

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