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Home » Solution: Let us define a function $ f(u) $ such that - Deep Underground Poetry

Solution: Let us define a function $ f(u) $ such that - Deep Underground Poetry

📅 May 2, 2026 👤 scraface

May 02, 2026

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🔥 Popular Posts

g(0) = d = \boxed{24}
Question: An entrepreneur designing a sustainable irrigation system mo...
Solution: The functional equation is:
f(x + y) + f(x - y) = 2f(x) + 2f(y), \quad \forall x, y \in \mathbb{R}
This is known as the **quadratic functional equation**. The general so...
Let $ f(x) = cx^2 $. Then:
f(x+y) + f(x-y) = c(x+y)^2 + c(x-y)^2 = c(x^2 + 2xy + y^2 + x^2 - 2xy...
So it satisfies the equation.
Given $ f(1) = c(1)^2 = 3 \Rightarrow c = 3 $, so $ f(x) = 3x^2 $.
Then $ f(5) = 3 \cdot 25 = \boxed{75} $

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