Areflection across the line y = x is represented by

Step-by-step explanation and

A reflection across the line y=x  (a line through the origin and at +45 degrees to the x-axis) is essentially an interchange of the x- and y-values, such as finding inverses.

For this reason, the reflection is usually represented by the operator

S_[x=y} : (x,y) ⇒ (y,x)

where _[...]  represents subscript (smaller letters near the bottom.

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step-by-step explanation: