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.