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📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 2Question: Let $ f $ be a function such that $ f(x^2 + 3) = 2x^4 + 10x^2 + 11 $. Find $ f(x^2 - 3) $.

📌 Solution: Let $ y = x^2 + 3 $. Then $ x^2 = y - 3 $. Substituting into the given equation:

📌 f(y) = 2(y - 3)^2 + 10(y - 3) + 11 = 2(y^2 - 6y + 9) + 10y - 30 + 11 = 2y^2 - 12y + 18 + 10y - 19 = 2y^2 - 2y - 1.

📌 Thus, $ f(x^2 - 3) = 2(x^2 - 3)^2 - 2(x^2 - 3) - 1 = 2(x^4 - 6x^2 + 9) - 2x^2 + 6 - 1 = 2x^4 - 12x^2 + 18 - 2x^2 + 5 = 2x^4 - 14x^2 + 23 $.

📌 Final answer: $\boxed{2x^4 - 14x^2 + 23}$

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