Here are the solutions to all the questions from the document on functions, compositions, and inverse functions:

Soal No. 1:

Given:
$f(x) = 2x^4 - 3x^3 + 12x - 5$
$g(x) = 10x^4 + 7x^3 - 11x^2 + 17x + 1$

To find $(f + g)(x)$:
$(f + g)(x) = f(x) + g(x)$ $(f + g)(x) = (2x^4 - 3x^3 + 12x - 5) + (10x^4 + 7x^3 - 11x^2 + 17x + 1)$ $= 12x^4 + 4x^3 - 11x^2 + 29x - 4$

Soal No. 2:

Given:
$f(x) = 6x^3 - 8x^2 + 9x - 15$
$g(x) = 12x^3 + 2x^2 + 3x$

To find $(f - g)(x)$:
$(f - g)(x) = f(x) - g(x)$ $(f - g)(x) = (6x^3 - 8x^2 + 9x - 15) - (12x^3 + 2x^2 + 3x)$ $= -6x^3 - 10x^2 + 6x - 15$

Soal No. 3:

Given:
$f(x) = 3x^2 + 7x - 5$
$g(x) = 4x^2 - 8x$

To find $(f \cdot g)(x)$:
$(f \cdot g)(x) = f(x) \cdot g(x)$ Multiply the two functions: $(f \cdot g)(x) = (3x^2 + 7x - 5)(4x^2 - 8x)$ Expanding: $= 12x^4 - 24x^3 + 28x^3 - 56x^2 - 20x^2 + 40x$ $= 12x^4 + 4x^3 - 76x^2 + 40x$

Soal No. 4:

Given:
$f(x) = 9x^2 + 18x$
$g(x) = 5x^2 - 24x$

To find $\frac{f(x)}{g(x)}$:
$\frac{f(x)}{g(x)} = \frac{9x^2 + 18x}{5x^2 - 24x}$ Factor both the numerator and denominator: $\frac{f(x)}{g(x)} = \frac{9x(x + 2)}{x(5x - 24)}$ Simplifying: $\frac{f(x)}{g(x)} = \frac{9(x + 2)}{5x - 24}$

Soal No. 5:

Given:
$f(x) = 2x^2 + 13x + 21$

To find $f(-8)$:
$f(-8) = 2(-8)^2 + 13(-8) + 21$ $= 2(64) - 104 + 21$ $= 128 - 104 + 21 = 45$

Would you like to explore any particular solution in detail or have additional questions?

Here are 5 related questions to practice:

1. How do you derive the inverse of a function?
2. What is the difference between function addition and function multiplication?
3. How is the domain affected in a function composition?
4. How do you compute the value of a composite function, such as $f(g(x))$?
5. What are the key properties of polynomial functions in algebra?

Tip: Always double-check the domain and range when working with composite or inverse functions to ensure the operations are valid!