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Evaluate the function \( f(x)=x^{2}-5 x+7 \) at the given values of the independent variable and simplify. \( \begin{array}{lll}\text { a. } f(6) & \text { b. } f(x+7) & \text { c. } f(-x)\end{array} \) \( \begin{array}{l}\text { a. } f(6)=\square \text { (Simplify your answer.) }\end{array} \)

Ask by Davison Herrera. in the United States
Feb 15,2025

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a. \( f(6) = 13 \) b. \( f(x + 7) = x² + 9x + 21 \) c. \( f(-x) = x² + 5x + 7 \)

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To evaluate \( f(x) = x^2 - 5x + 7 \) at the given values, let's calculate each one step-by-step: a. For \( f(6) \): \[ f(6) = 6^2 - 5(6) + 7 \] \[ = 36 - 30 + 7 \] \[ = 6 + 7 = 13 \] So, \( f(6) = 13 \). b. For \( f(x+7) \): \[ f(x+7) = (x+7)^2 - 5(x+7) + 7 \] \[ = (x^2 + 14x + 49) - (5x + 35) + 7 \] \[ = x^2 + 14x + 49 - 5x - 35 + 7 \] \[ = x^2 + (14x - 5x) + (49 - 35 + 7) \] \[ = x^2 + 9x + 21 \] c. For \( f(-x) \): \[ f(-x) = (-x)^2 - 5(-x) + 7 \] \[ = x^2 + 5x + 7 \] Final outputs: a. \( f(6) = 13 \) b. \( f(x+7) = x^2 + 9x + 21 \) c. \( f(-x) = x^2 + 5x + 7 \)

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