Food Stamps Fraud Alert: How Millions Are Being Overcharged Every Day

Food Stamps Fraud Alert: How Millions Are Being Overcharged Every Day

**Food Stamps Fraud Alert: How Millions Are Being Overcharg

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\[ h(x^2 - 2) = 3\sqrt{(x^2 - 2) - 2} + 5 = 3\sqrt{x^2 - 4} + 5. \]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:\[ f(a + b) = f(a) + f(b), \]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: