Math Problem Statement
Solve this with solution
Evaluate f(x) = 6x^2 - 5x + 3 at x = 3, g(x) = 6x + 6 at x = -1, f(x) = x^2 - 3x + 1 at x = 2, g(x) = 4x^3 + 5x^2 - 7x + 6 at x = 5, f(x) = 20x^2 - 95x + 40 at x = -4.
Solution
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1. at
= 6(9) - 15 + 3 = 54 - 15 + 3 = 42$$ So, $$f(3) = 42$$. --- ### 2. $$g(x) = 6x + 6$$ at $$x = -1$$ $$g(-1) = 6(-1) + 6 = -6 + 6 = 0$$ So, $$g(-1) = 0$$. --- ### 3. $$f(x) = x^2 - 3x + 1$$ at $$x = 2$$ $$f(2) = (2)^2 - 3(2) + 1 = 4 - 6 + 1 = -1$$ So, $$f(2) = -1$$. --- ### 4. $$g(x) = 4x^3 + 5x^2 - 7x + 6$$ at $$x = 5$$ $$g(5) = 4(5)^3 + 5(5)^2 - 7(5) + 6 = 4(125) + 5(25) - 7(5) + 6 = 500 + 125 - 35 + 6 = 596$$ So, $$g(5) = 596$$. --- ### 5. $$f(x) = 20x^2 - 95x + 40$$ at $$x = -4$$ $$f(-4) = 20(-4)^2 - 95(-4) + 40 = 20(16) + 380 + 40 = 320 + 380 + 40 = 740$$ So, $$f(-4) = 740$$. --- ### Summary of Results: 1. $$f(3) = 42$$ 2. $$g(-1) = 0$$ 3. $$f(2) = -1$$ 4. $$g(5) = 596$$ 5. $$f(-4) = 740$$ Let me know if you'd like more details or have any questions! Here are some related questions to extend this: 1. How do you find the derivative of a polynomial function? 2. What is the significance of evaluating functions at certain points? 3. How would the solution change if you had $$f(x) = 6x^2 - 5x + 3$$ but at $$x = -3$$? 4. How do you apply these methods to real-world problems, such as in physics? 5. What happens when you evaluate rational functions instead of polynomial functions? **Tip:** Always substitute values carefully and simplify step by step to avoid mistakes in calculation.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Polynomials
Function Evaluation
Formulas
f(x) = ax^2 + bx + c
g(x) = ax^3 + bx^2 + cx + d
Theorems
Substitution
Suitable Grade Level
Grades 9-11
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