Question 1181200
<pre>
The red graph is the graph of f(x) = 2x<sup>3</sup>+1
The dotted line is the identity line y=x 
The green graph is the inverse <font size=4>f<sup>-1</sup></font>(x) = {{{root(3,(x-1)/2)}}}

Note that the inverse of a function is its reflection in or across the
identity line.

{{{drawing(400,400,-5,5,-5,5,

graph(400,400,-5,5,-5,5,11,((x-1)/2)^(1/3)),

graph(400,400,-5,5,-5,5,10,-(-(x-1)/2)^(1/3)),
 

graph(400,400,-5,5,-5,5,2x^3+1,10,11,12,x*sqrt(sin(9x))/sqrt(sin(9x)))

 ))}}}


{{{f(x)=2x^3+1}}}
{{{y=2x^3+1}}}
{{{x=2y^3+1}}}
{{{x-1=2y^3}}}
{{{(x-1)/2=y^3}}}

{{{root(3,(x-1)/2)=y}}}
<font size=4>f<sup>-1</sup></font>(x) = {{{root(3,(x-1)/2)}}}

Edwin</pre>