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Home » How Dig Digged Uncovered the Most Unexpected Treasure in Town - Groen Casting

How Dig Digged Uncovered the Most Unexpected Treasure in Town - Groen Casting

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 Solution: To solve for \( h(x^2 - 2) \), start with the given function:

📌 \[ h(x^2 + 2) = 3x + 5. \]

📌 Let \( u = x^2 + 2 \). Then, \( h(u) = 3\sqrt{u - 2} + 5 \). We want to find \( h(x^2 - 2) \), so set \( u = x^2 - 2 \). Then,

📌 \[ h(x^2 - 2) = 3\sqrt{(x^2 - 2) - 2} + 5 = 3\sqrt{x^2 - 4} + 5. \]

📌 Thus, \( h(x^2 - 2) \) is:

📌 \boxed{3\sqrt{x^2 - 4} + 5}

📌 Question: For all real numbers \( a, b, c \), find the number of functions \( f: \mathbb{R} \to \mathbb{R} \) such that \( f(a + b) = f(a) + f(b) \) and \( f \) is linear.

📌 Solution: A function \( f: \mathbb{R} \to \mathbb{R} \) is linear if it can be expressed as \( f(x) = kx \) for some constant \( k \). Given the functional equation:

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