The given equation is:

$x = \pm \sqrt{1 - y}$

This represents a relationship between $x$ and $y$, where the value of $x$ depends on $y$, and you take both the positive and negative square roots.

Key steps to interpret this equation:

1. Square Root Component: $\sqrt{1 - y}$ means that the expression inside the square root, $1 - y$, must be non-negative (i.e., $1 - y \geq 0$), otherwise, the result would be complex.

   $1 - y \geq 0 \quad \Rightarrow \quad y \leq 1$

2. Positive and Negative Solutions: The $\pm$ sign indicates that there are two possible values for $x$: one where $x$ is the positive square root of $1 - y$, and the other where $x$ is the negative square root.

Thus, the equation can be rewritten as: $x = +\sqrt{1 - y} \quad \text{or} \quad x = -\sqrt{1 - y}$

The domain of this function is restricted to $y \leq 1$ to ensure that the square root remains real.

Would you like me to further expand on this topic or explore any specific applications or transformations of the equation?

5 Related Questions:

1. How would you solve for $y$ in terms of $x$ from the given equation?
2. What is the domain and range of this equation?
3. Can you graph the function $x = \pm \sqrt{1 - y}$?
4. How would this equation change if the $\pm$ sign was removed?
5. How do you handle the case when $y > 1$ in similar equations?

Tip:

When dealing with square roots in equations, always ensure that the expression under the root is non-negative to avoid complex solutions.