What transformation transforms (p, q) to (q, p)?

Question

a reflection over the y-axis

a rotation of 90° about the origin

a reflection over the x-axis

a reflection over y = x

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Answer 1 · 2016-10-26T09:38:05

If we wish to map #p->q# and #q->p#, we are inverting the function. An inversion can be accomplished by reflecting over #y = x#.

For example, take #y = x^2#. Now switch #y# and #x#, and solve for #y#.

#x = y^2#

#y = pmsqrt(x)#

Both (#pm#) of these functions then combine to form the inverse.

Original
graph{x^2 [-10, 10, -5, 5]}

Inverse (#(p,q) -> (q,p)#)
graph{(y - sqrt(x))(y + sqrt(x)) = 0 [-10, 10, -5, 5]}