Problem 125 - Precalculus Essentials

Question

$$\text { Solve for } y: \quad x=y^{2}-1, y \geq 0$$

Step-by-Step Solution

Answer

The solution is \(y = \sqrt{x + 1}\)

Step 1: Isolate y

The given equation is \(x = y^2 - 1\). To solve for \(y\), rewrite the equation as \(y^2 = x + 1\)

Step 2: Square Root Both Sides

To get \(y\) alone, take the square root of both sides. This results in two solutions: \(y = \sqrt{x + 1}\) and \(y = -\sqrt{x + 1}\)

Step 3: Consider the Restriction on y

The problem specifies that \(y \geq 0\). Therefore, the negative solution (-\sqrt{x + 1}) does not apply. The only valid solution is \(y = \sqrt{x + 1}\)