Question 1179041


{{{f(x) = 3sqrt (x) + 4}}}

find {{{f^-1}}}

{{{y =  3sqrt (x) + 4}}}

{{{x=  3sqrt (y) + 4}}}

{{{3sqrt (y)= x-4}}}

{{{sqrt (y)=(x-4)/3}}}

{{{(sqrt (y))^2=((x-4)/3)^2}}}

{{{y=(x-4)^2/9}}}

{{{f^-1=(1/9)(x-4)^2}}}


domain of f(x) :

{ {{{x}}} element {{{R}}} : {{{x>=0}}} } 

interval: [{{{0}}},{{{infinity}}})

range  of f(x) :

{ {{{f}}} element{{{ R}}} : {{{f>=4}}} }

interval: [{{{4}}},{{{infinity}}})



domain of f^-1(x) :

{{{R}}} , all real numbers

range:

{ {{{f}}} element{{{ R}}} : {{{f>=0}}} }

interval: [{{{0}}},{{{infinity}}})
{{{drawing(600,600,-10,10,-10,10, 

graph(600,600,-10,10,-10,10,11, 3sqrt (x) + 4),
graph(600,600,-10,10,-10,10,(1/9)(x-4)^2*sqrt(sin(7x))/sqrt(sin(7x) )),

red(locate(4,-2,f^-1(x)=(1/9)(x-4)^2)), green(locate(-5,3,f(x)=3sqrt (x) + 4))   )}}}