 
*f*(*x*) = *x*2 − 3*x* + 9 f(-x)

To find \( f(-x) \) when \( f(x) = x^2 - 3x + 9 \), substitute \( -x \) into the function wherever \( x \) appears.

Given:
\[
f(x) = x^2 - 3x + 9
\]
Substitute \( -x \) for \( x \):
\[
f(-x) = (-x)^2 - 3(-x) + 9
\]

Now, simplify each term:
\[
f(-x) = x^2 + 3x + 9
\]

So, \( f(-x) = x^2 + 3x + 9 \).

Would you like more details or have any questions?

Here are 5 related questions for practice:

1. What is \( f(x+1) \) if \( f(x) = x^2 - 3x + 9 \)?
2. How do you find the value of \( f(-2) \) for \( f(x) = x^2 - 3x + 9 \)?
3. What is \( 2f(x) \) if \( f(x) = x^2 - 3x + 9 \)?
4. What is the symmetry of the function \( f(x) = x^2 - 3x + 9 \)?
5. How do you find the roots of the equation \( f(x) = 0 \) for \( f(x) = x^2 - 3x + 9 \)?

**Tip:** When substituting \(-x\) into a function, remember that squaring \(-x\) gives \(x^2\) and that multiplying \(-x\) by a negative coefficient changes the sign.

Learn how to evaluate f(-x) for the quadratic function f(x) = x^2 - 3x + 9. Understand the process of substituting -x into the function, simplifying the expression, and solving for f(-x). Suitable for high school students and those preparing for advanced algebra.

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