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In the provided image, two functions \( f(x) \) and \( g(x) \) are given, and you are asked to determine:

a. \( f(x) + g(x) \)  
b. \( f(x) - g(x) \)

The given functions are:
\[
f(x) = 4x^3 - x^2 + 8x - 1
\]
\[
g(x) = 4x^3 + 2x^2 - 10x + 5
\]

### a. \( f(x) + g(x) \)
To add the two functions, sum their corresponding terms:
\[
f(x) + g(x) = (4x^3 - x^2 + 8x - 1) + (4x^3 + 2x^2 - 10x + 5)
\]
Simplify by combining like terms:
\[
(4x^3 + 4x^3) + (-x^2 + 2x^2) + (8x - 10x) + (-1 + 5)
\]
\[
= 8x^3 + x^2 - 2x + 4
\]

So, the result is:
\[
f(x) + g(x) = 8x^3 + x^2 - 2x + 4
\]

### b. \( f(x) - g(x) \)
To subtract the two functions, subtract their corresponding terms:
\[
f(x) - g(x) = (4x^3 - x^2 + 8x - 1) - (4x^3 + 2x^2 - 10x + 5)
\]
Distribute the negative sign and combine like terms:
\[
(4x^3 - 4x^3) + (-x^2 - 2x^2) + (8x + 10x) + (-1 - 5)
\]
\[
= 0x^3 - 3x^2 + 18x - 6
\]

So, the result is:
\[
f(x) - g(x) = -3x^2 + 18x - 6
\]

---

Do you need any further clarifications or details?

Here are 5 related questions:
1. What is the degree of the polynomial \( f(x) + g(x) \)?
2. Can you factor \( f(x) + g(x) \)?
3. What are the zeros of \( f(x) - g(x) \)?
4. How would you graph \( f(x) + g(x) \) and \( f(x) - g(x) \)?
5. How does the result change if we multiply both functions by a constant?

**Tip:** When adding or subtracting functions, always align the terms based on the degree of the variables to combine them easily.

Diketahui f(x) = 4x^3 - x^2 + 8x - 1 dan g(x) = 4x^3 + 2x^2 - 10x + 5. Tentukan: a. f(x) + g(x), b. f(x) - g(x)

Learn how to solve polynomial functions by performing addition and subtraction. This detailed explanation walks through solving f(x) = 4x^3 - x^2 + 8x - 1 and g(x) = 4x^3 + 2x^2 - 10x + 5. Understand key algebraic concepts and polynomial operations. Ideal for Grades 9-12.

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