COPYRIGHT NOTICE
Copyright 2007 Samuel Dagan
dagan@post.tau.ac.il
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Inversion of a quadratic function
The origin of the figure is at (0,0)
© Samuel Dagan
Inverse quadratic
x
y
x
y
x
y
The single-valued function
y=x²
is defined for all values of x .
The plotted interval
is |x|≤1 , and both
axes have identical scales.
The function on the right and its
coordinate system will be inverted next by
an upside-down rotation in
3-dimensions, about the dashed line y=x .
If we denote the abscissa
of the inverse function by x, and
the
ordinate -
by y, the inverse
function is y
= ±√x with
the domain of x ≥0 .
y
= ±√x
is double-valued for x>0
and is single-valued for x=0 .
Notice that by renaming the coordinate
axes after the inversion, the coordinate
system remains right-handed. The
inversion of the axes was not necessary.
The inversion of the function on the
left will be obtained next by a mirror
reflection along the dashed line, without
reflecting the coordinate axes.
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