If f, of, x, equals, 4, start superscript, 3, x, end superscript, minus, 1f(x)=4 
3x
 −1, what is the value of f, of, 2f(2), to the nearest ten-thousandth (if necessary)?

We are given the function \( f(x) = 4^{3x - 1} \) and need to find the value of \( f(2) \).

### Step-by-step solution:

1. First, substitute \( x = 2 \) into the function:
   \[
   f(2) = 4^{3(2) - 1}
   \]

2. Simplify the exponent:
   \[
   f(2) = 4^{6 - 1} = 4^5
   \]

3. Now, calculate \( 4^5 \):
   \[
   4^5 = 4 \times 4 \times 4 \times 4 \times 4 = 1024
   \]

Thus, \( f(2) = 1024 \).

Since no rounding is needed, the value of \( f(2) \) is \( \boxed{1024} \).

Let me know if you need further clarification! Here are 5 related questions to explore:

1. What is \( f(3) \) for the same function?
2. How would the result change if the base were 3 instead of 4?
3. Can you find the inverse function of \( f(x) \)?
4. What is the derivative of \( f(x) \) with respect to \( x \)?
5. If \( f(x) = 1024 \), what is the value of \( x \)?

**Tip:** When solving functions involving exponents, make sure to simplify the exponent first to make the calculations easier!

If f(x) = 4^(3x - 1), what is the value of f(2), to the nearest ten-thousandth (if necessary)?

Explore how to find the value of an exponential function, f(x) = 4^(3x - 1), by substituting x = 2 and simplifying the exponent. This step-by-step guide demonstrates the use of exponential properties to find f(2), suitable for high school students in Grades 9-12.

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