To find the inverse of the relation given by the equation \( y = \sqrt{x} \), we need to follow these steps:
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Switch the variables: Replace \( y \) with \( x \) and \( x \) with \( y \).
This gives us: \[ x = \sqrt{y} \]
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Solve for \( y \): To isolate \( y \), we square both sides of the equation to eliminate the square root.
\[ x^2 = y \]
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Express the inverse relation: The equation we found describes the inverse relation.
Thus, the inverse of the relation \( y = \sqrt{x} \) is: \[ y = x^2 \]
So, the inverse relation is \( y = x^2 \).