To evaluate the function \( f(x-1) = x^2 + 6x + 4 \), we need to find the original function \( f(x) \). To do this, we can substitute \( u = x - 1 \), so \( x = u + 1 \).

1. Substitute \( x = u + 1 \) into the given function:
   \[
   f(u) = (u+1)^2 + 6(u+1) + 4
   \]

2. Expand the expression:
   \[
   f(u) = (u^2 + 2u + 1) + (6u + 6) + 4
   \]

3. Simplify by combining like terms:
   \[
   f(u) = u^2 + 2u + 1 + 6u + 6 + 4 = u^2 + 8u + 11
   \]

Thus, the original function is:
\[
f(x) = x^2 + 8x + 11
\]

Would you like more details or have any questions about this solution? Here are some related questions you might find interesting:

1. How would you evaluate \( f(x+2) \) if \( f(x) = x^2 + 8x + 11 \)?
2. Can you find the vertex of the parabola represented by \( f(x) = x^2 + 8x + 11 \)?
3. What are the roots of the function \( f(x) = x^2 + 8x + 11 \)?
4. How does the graph of \( f(x) = x^2 + 8x + 11 \) compare to the graph of \( f(x) = x^2 \)?
5. What is the y-intercept of the function \( f(x) = x^2 + 8x + 11 \)?
6. How would you determine the axis of symmetry for \( f(x) = x^2 + 8x + 11 \)?
7. Can you express \( f(x) = x^2 + 8x + 11 \) in vertex form?
8. What is the minimum value of \( f(x) = x^2 + 8x + 11 \)?

**Tip:** When dealing with functions, substituting and simplifying carefully is key to finding the correct form of the function.

Learn how to evaluate the function f(x-1)=x^2+6x+4 step-by-step. Understand the process of substitution and simplification to find the original function. Suitable for high school students in Grades 10-12.

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