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We are given a piecewise function \( f(x) \):

\[
f(x) = 
\begin{cases} 
\frac{1}{x}, & \text{jika } x > 3 \\
2x, & \text{jika } x \leq 3 
\end{cases}
\]

We are asked to determine the values of:

1. \( f(-4) \)
2. \( f(0) \)
3. \( f(t^2 + 5) \)

### a. \( f(-4) \)
Since \(-4 \leq 3\), we use the second part of the function, \( f(x) = 2x \). Thus:

\[
f(-4) = 2(-4) = -8
\]

### b. \( f(0) \)
Since \( 0 \leq 3 \), we again use \( f(x) = 2x \). Thus:

\[
f(0) = 2(0) = 0
\]

### c. \( f(t^2 + 5) \)
We need to determine which part of the function applies to \( f(t^2 + 5) \). Since \( t^2 + 5 > 3 \) for any real number \( t \), we use the first part of the function, \( f(x) = \frac{1}{x} \). Thus:

\[
f(t^2 + 5) = \frac{1}{t^2 + 5}
\]

### Final Answers:
a. \( f(-4) = -8 \)  
b. \( f(0) = 0 \)  
c. \( f(t^2 + 5) = \frac{1}{t^2 + 5} \)

Would you like further details or have any questions?

Here are five related questions for deeper understanding:
1. What happens if \( t = -2 \) in part c?
2. How does the behavior of the piecewise function change around \( x = 3 \)?
3. What is \( f(5) \) based on the given function?
4. How would you express \( f(x) \) if \( x = 3 \)?
5. Can you find the derivative of \( f(x) \) for \( x > 3 \)?

**Tip:** Always check the conditions in a piecewise function carefully before selecting the right expression for a given input.

Diketahui: f(x) = (1/x jika x > 3, 2x jika x <= 3). Tentukan nilai dari: a. f(-4), b. f(0), c. f(t^2 + 5).

Learn how to evaluate a piecewise function where f(x) is defined as 1/x for x > 3 and 2x for x <= 3. This problem covers key concepts of algebra and piecewise functions, suitable for Grades 10-12.

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