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Home » Is Your Home Infested? Spider-Like Baby Termites Are Spreading Faster Than You Realize! - Upplift

Is Your Home Infested? Spider-Like Baby Termites Are Spreading Faster Than You Realize! - Upplift

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 f(x+1) - f(x) = 6x + 4

📌 2a = 6 \Rightarrow a = 3, \quad a + b = 4 \Rightarrow 3 + b = 4 \Rightarrow b = 1

📌 Thus, the leading coefficient of $ f(x) $ is $ \boxed{3} $.

📌 Question: A function $ f: \mathbb{R} \to \mathbb{R} $ satisfies $ f(a + b) + f(a - b) = 2f(a) + 2f(b) $ for all real $ a, b $. If $ f(1) = 1 $, find $ f(2) $.

📌 Solution: Let’s plug in $ a = b = 1 $ into the functional equation:

📌 f(2) + f(0) = 2f(1) + 2f(1) = 4

📌 We are given $ f(1) = 1 $, so:

📌 f(2) + f(0) = 4 \quad \text{(1)}

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and $ L $ is a multiple of 7 (since pipes are seven units long and tot...
L \equiv 1 \pmod{13} \quad ext{and} \quad L \equiv 0 \pmod{7}
L \equiv 0 \pmod{7} \
Use the Chinese Remainder Theorem. Let $ L = 7k $. Substitute into the...
7k \equiv 1 \pmod{13}
We solve for $ k $: find the modular inverse of 7 modulo 13.
$ 7 \cdot 1 = 7
$ 7 \cdot 2 = 14 \equiv 1 \pmod{13} $
So $ 7^{-1} \equiv 2 \pmod{13} $
k \equiv 2 \pmod{13} \Rightarrow k = 13m + 2

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