https://r2.erweima.ai/mathbot/image/17266159014912si1as96.jpg

The image contains a mathematical function \( f(x) \), which appears as:

\[
f(x) = -\sqrt{\frac{18}{x^4}} = -\frac{\sqrt{18}}{x^2}
\]

To simplify:

1. \( \sqrt{18} = \sqrt{9 \times 2} = 3\sqrt{2} \)

So the function simplifies to:

\[
f(x) = -\frac{3\sqrt{2}}{x^2}
\]

This is the simplified expression for \( f(x) \).

Do you want further details or have any questions?

Here are five related questions to explore further:
1. How do you compute the derivative of \( f(x) = -\frac{3\sqrt{2}}{x^2} \)?
2. What is the domain of \( f(x) = -\frac{3\sqrt{2}}{x^2} \)?
3. How would you graph \( f(x) = -\frac{3\sqrt{2}}{x^2} \)?
4. What are the asymptotes of \( f(x) = -\frac{3\sqrt{2}}{x^2} \)?
5. How does the function behave as \( x \to 0 \) and as \( x \to \infty \)?

**Tip:** When simplifying expressions with square roots, factor the number under the root to identify perfect squares.

Simplify the function f(x) = -√(18/x^4).

This problem demonstrates how to simplify the function f(x) = -√(18/x^4), covering key algebraic concepts such as square root simplification and the use of exponent properties. Suitable for students in Grades 10-12.

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