Question 1057054
<pre><b>
The inverse of the point (1,2) which is found
by interchanging the two coordinates (2,1).  It
always amounts to a reflection in the 45-degree
line through the origin, the line whose equation is 
y = x.  The red curve and the green curves below
are inverses of each other.  The red curve is the
graph of f and green curve is the graph of f<sup>-1</sup>.

The dotted blue line is the line y = x, which is 
often called "the identity line".  The graph of f, 
the red curve, contains the point (1,2) and the 
graph of f<sup>-1</sup>, the green curve, contains 
the inverse point (2,1), where the coordinates are
interchanged.

{{{drawing(400,400,-3.6,3.6,-3.6,3.6,  graph(400,400,-3.6,3.6,-3.6,3.6,2x^3),
 graph(400,400,-3.6,3.6,-3.6,3.6,10,(x/2)^(1/3)),
circle(1,2,.05), circle(2,1,.05), locate(1,2,"(1,2)"), locate(2,1,"(2,1)"),
 graph(400,400,-3.6,3.6,-3.6,3.6,10,-(-x/2)^(1/3),
x*sqrt(sin(10x))/sqrt(sin(10x))

)
)}}}

Edwin</pre></b>