Question 1135210

{{{f(x)=6-3x^2}}},if {{{x<0}}}

find the inverse of the one to one function

{{{f^-1(x)}}}

since {{{f (x)=y}}}, we have

{{{y=6-3x^2}}}.......swap {{{x}}} and {{{y}}}

{{{x=6-3y^2}}}........solve for {{{y}}}

{{{3y^2=6-x}}}

{{{y^2=(6-x)/3}}}

{{{y=sqrt((6-x)/3)}}}

{{{f^-1(x)=sqrt((6-x)/3)}}}

so your inverse is: {{{y=sqrt((6-x)/3)}}} or {{{y=-sqrt((6-x)/3)}}} 

and it is  one to one function


{{{ graph( 600, 600, -10, 10, -10, 10,6-3x^2, sqrt((6-x)/3), -sqrt((6-x)/3)) }}}