Let's analyze the problem and solve it.

The given equation is: $4f(x) + 2f(-x) = 5x + 3$ where $f(x)$ is a linear function.

1. We know that a linear function can be written as $f(x) = ax + b$, where $a$ and $b$ are constants.

2. Let’s substitute $f(x) = ax + b$ and $f(-x) = -ax + b$ into the equation: $4(ax + b) + 2(-ax + b) = 5x + 3$ Expanding both sides: $4(ax + b) = 4ax + 4b$ $2(-ax + b) = -2ax + 2b$ Now combine the terms: $(4ax - 2ax) + (4b + 2b) = 5x + 3$ Simplify: $2ax + 6b = 5x + 3$ By comparing the coefficients of $x$ and the constants, we get: $2a = 5 \quad \text{and} \quad 6b = 3$ Solving these equations: $a = \frac{5}{2}, \quad b = \frac{1}{2}$

Thus, the function is: $f(x) = \frac{5}{2}x + \frac{1}{2}$

Now, let's check the statements:

1. $f(1) = -3$: $f(1) = \frac{5}{2}(1) + \frac{1}{2} = \frac{5}{2} + \frac{1}{2} = 3 \quad (\text{not } -3)$ False

2. $f^{-1}(8) = 3$: To find the inverse of $f(x) = \frac{5}{2}x + \frac{1}{2}$, we solve for $x$: $y = \frac{5}{2}x + \frac{1}{2}$ Solve for $x$: $2y = 5x + 1 \quad \Rightarrow \quad 5x = 2y - 1 \quad \Rightarrow \quad x = \frac{2y - 1}{5}$ The inverse function is: $f^{-1}(y) = \frac{2y - 1}{5}$ Now, substitute $y = 8$: $f^{-1}(8) = \frac{2(8) - 1}{5} = \frac{16 - 1}{5} = \frac{15}{5} = 3$ True

3. $f(-3) = 1$: $f(-3) = \frac{5}{2}(-3) + \frac{1}{2} = -\frac{15}{2} + \frac{1}{2} = -\frac{14}{2} = -7$ False

4. $f^{-1}(-2) = -1$: Substitute $y = -2$ into the inverse function: $f^{-1}(-2) = \frac{2(-2) - 1}{5} = \frac{-4 - 1}{5} = \frac{-5}{5} = -1$ True

Conclusion:

Statements 2 and 4 are true. Therefore, the correct answer is C: 2 and 4 SAJA yang benar.

Would you like any further details or clarifications? Here are five related questions:

1. How is the inverse function of a linear function generally derived?
2. What does it mean for a function to be linear?
3. What is the significance of the slope $a$ in the linear function $f(x) = ax + b$?
4. How does the inverse function reflect the original function graphically?
5. How can you verify if a function has an inverse?

Tip: Always check the inverse function by plugging the result back into the original function.