Grades 11-12 Video Solutions 2023-2023_11-12

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Video Summary

The problem involves two functions, \( f \) and \( g \), satisfying a system of equations with variables \( x \) and \( 1-x \). By substituting \( 1-x \) in place of \( x \) in the second equation, we simplify and find expressions for \( f(x) \) and \( g(1-x) \). Assigning variables \( a = f(x) \) and \( b = g(1-x) \), we solve the algebraic system: \( a + 2b = x^2 \) and \( a - b = x^2 - 2x + 1 \). Solving these, \( f(x) = x^2 - \frac{4}{3}x + \frac{2}{3} \). The solution corresponds to choice A.