The function given is \( f(x) = x^2 - 5x + 6 \).
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Finding the solutions to the equation when \( f(x) = 6 \): We want to solve \( f(x) = 6 \):
\[ x^2 - 5x + 6 = 6 \]
Simplifying this:
\[ x^2 - 5x + 6 - 6 = 0 \implies x^2 - 5x = 0 \]
Factoring:
\[ x(x - 5) = 0 \]
Therefore, the solutions are:
\[ x = 0 \quad \text{or} \quad x = 5 \]
Thus, the solutions to the equation \( f(x) = 6 \) are the points \((0, 6)\) and \((5, 6)\).
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Finding the solutions to the equation when \( f(2) \) and \( f(3) \): First, we evaluate \( f(2) \) and \( f(3) \):
\[ f(2) = 2^2 - 5(2) + 6 = 4 - 10 + 6 = 0 \] \[ f(3) = 3^2 - 5(3) + 6 = 9 - 15 + 6 = 0 \]
Therefore:
- The solution to the equation when \( f(2) = 0 \) is the point \((2, 0)\).
- The solution to the equation when \( f(3) = 0 \) is the point \((3, 0)\).
Thus, the solutions to the equation when \( f(2) \) and \( f(3) \) are the points \((2, 0)\) and \((3, 0)\).