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Home » Short Fringe Makeover: How Cutesy Short Hair Took Over Instagram Overnight! - Aurero

Short Fringe Makeover: How Cutesy Short Hair Took Over Instagram Overnight! - Aurero

📅 March 15, 2026 👤 scraface

Mar 15, 2026

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📌 \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:

📌 \[ f(a + b) = f(a) + f(b), \]

📌 assuming linearity, the function satisfies this by the very definition of linearity (additivity and homogeneity). Thus, the only functions meeting the criteria are those of the form \( f(x) = kx \). Since \( k \) can be any real number, there are infinitely many such linear functions, one for each real number \( k \). Therefore, the number of such functions is:

📌 \boxed{\infty}

📌 Question: The perimeter of a rectangle is 50. What is the largest possible area of the rectangle?

📌 Solution: Let the length and width of the rectangle be \( l \) and \( w \), respectively. The perimeter is given by:

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