https://file.aiquickdraw.com/mathbot/file/17263315081599clv2lvk.jpg

The given function from the image is:

\[
f(-x) = 3(-x)^4 - 7(-x)^2 + 9
\]

### Simplification:
We will simplify each term step by step.

1. \((-x)^4 = x^4\) because raising a negative number to an even power gives a positive result.
2. \((-x)^2 = x^2\) for the same reason (even power).

So, the function becomes:

\[
f(-x) = 3x^4 - 7x^2 + 9
\]

This is the simplified form of the function.

Would you like to explore more details, such as analyzing its symmetry, derivative, or behavior? Here are some related questions to consider:

1. What is the symmetry of this function?
2. What is the derivative of this function?
3. How do we find the critical points of this function?
4. Can this function be factored?
5. What are the real roots of this function?

**Tip:** Remember, even-powered terms like \(x^4\) and \(x^2\) often result in even functions, which are symmetric around the y-axis!

Learn how to simplify the polynomial function f(-x) = 3(-x)^4 - 7(-x)^2 + 9. This step-by-step solution covers key concepts such as even powers and function simplification, suitable for students in Grades 10-12.

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