Answer:
To solve \( 1 = x^2 \) for \( x \), we need to take the square root of both sides of the equation.
\[
\begin{align*}
1 &= x^2 \\
\sqrt{1} &= \sqrt{x^2} \\
1 &= |x|
\end{align*}
\]
Now, \( |x| = 1 \) implies that \( x \) could be either \( 1 \) or \( -1 \).
For the equation \( y = x^2 - 1 \), you just need to subtract 1 from both sides of the equation to isolate \( x^2 \):
\[
\begin{align*}
y + 1 &= x^2 \\
x &= \pm \sqrt{y + 1}
\end{align*}
\]
So, the solutions for \( x \) in terms of \( y \) are \( x = \sqrt{y + 1} \) and \( x = -\sqrt{y + 1} \).
