Yes, it's perfectly fine to write \( \tan^{-1}(y) = x \). This is another way of expressing the inverse tangent (or arctangent) function, which is commonly used in mathematics. Both notations \( \tan^{-1}(y) \) and \( \arctan(y) \) mean the same thing: the angle \( x \) whose tangent is \( y \).

So, the equation \( \tan^{-1}(y) = x \) correctly represents the same relationship as \( x = \arctan(y) \).

Would you like to know more about the notation, or do you have any other questions?

Here are some related questions to consider:

1. What are the properties of the \( \tan^{-1}(x) \) function?
2. How do you find the derivative of \( \tan^{-1}(y) \)?
3. Can you solve \( \tan^{-1}(2x) = \frac{\pi}{4} \) for \( x \)?
4. How does \( \tan^{-1}(x) \) differ from \( \tan(x) \) in terms of their ranges and domains?
5. How can you express other inverse trigonometric functions using similar notation?

**Tip:** When using \( \tan^{-1}(y) \), make sure that you're clear it's the inverse function, not the reciprocal, which is a common point of confusion for some learners.

Explore the equation \( \tan^{-1}(y) = x \), its significance in inverse trigonometric functions, and its relationship to \( \arctan(y) \). This page provides a detailed explanation suitable for advanced high school students and beyond.

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