Question 1197339
{{{f(x)=6x^2+11}}}

to determine the equation of the inverse for the quadratic equation, recall that {{{ f(x)=y}}}  

{{{y=6x^2+11}}}...... swap variables

{{{x=6y^2+11}}}..........solve for {{{y}}}

{{{x-11=6y^2}}}

{{{(x-11)/6=y^2}}}

{{{y=sqrt((x-11)/6)}}}
 
{{{y}}}=± {{{sqrt(x - 11)/sqrt(6)}}}


so, inverse is

{{{f}}}'{{{(x)}}}= ± {{{sqrt(x - 11)/sqrt(6)}}}



{{{ graph( 600, 600, -10, 25, -10, 25, 6x^2+11,sqrt(x - 11)/sqrt(6),-sqrt(x - 11)/sqrt(6)) }}}