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Chapter 1: Problem 125

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

Short Answer

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

Step by step solution

01

Isolate y

The given equation is \(x = y^2 - 1\). To solve for \(y\), rewrite the equation as \(y^2 = x + 1\)
02

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 \(y = -\sqrt{x + 1}\)
03

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 \(y = \sqrt{x + 1}\)

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