Rearrange formulas to highlight a chosen quantity across the expression types studied.
Rearrange a radical formula with branches and real conditions
Problem
In \(y~=~\sqrt{x~+~3}\), isolate \(x\). State the output condition, branch count, and reason.
Big Picture
What this problem is really about
Record the principal square root's nonnegative output condition before reversing the formula. Squaring then removes the radical, and a final subtraction isolates the original input. No plus-or-minus branch belongs on that input because the squared output determines it uniquely; the branch information is already carried by the requirement that the original output be nonnegative.
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