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### 1. \( f(x) = 6x^2 - 5x + 3 \) at \( x = 3 \)

\[
f(3) = 6(3)^2 - 5(3) + 3
= 6(9) - 15 + 3
= 54 - 15 + 3
= 42
\]

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.

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.

Learn how to evaluate polynomial functions like f(x) = 6x^2 - 5x + 3, g(x) = 6x + 6, and others at specific values of x. Suitable for high school students, Grades 9-11. Includes step-by-step solutions.

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