It seems like you're asking to evaluate a function \( f(x) \) based on the equation:

\[
f(6) = 12x + 1
\]

To help clarify, did you mean the function is defined as \( f(x) = 12x + 1 \)? And are you asking to evaluate it at \( x = 6 \)?

If so, we can substitute \( x = 6 \) into the equation.

\[
f(6) = 12(6) + 1 = 72 + 1 = 73
\]

Thus, \( f(6) = 73 \).

Would you like more details or have any questions? Here are some related questions for further exploration:

1. What is \( f(x) \) for another value of \( x \)?
2. How do we solve \( f(x) = 0 \) for \( x \)?
3. What happens to \( f(x) \) as \( x \) approaches infinity?
4. Can you find the inverse of \( f(x) = 12x + 1 \)?
5. What is the slope of the line represented by \( f(x) \)?

**Tip**: In linear functions like \( f(x) = 12x + 1 \), the coefficient of \( x \) (here 12) is the slope, and the constant (1) is the y-intercept.

Discover how to evaluate the linear function f(x) = 12x + 1 at x = 6, using simple algebraic substitution. This example provides a clear step-by-step solution, demonstrating core concepts in linear functions. Suitable for students in Grades 6-8.

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