Question 1179076
{{{f(x) = x^3 - 2}}}

table

{{{x}}}|{{{f(x)}}} 


{{{0}}}|{{{-2}}} ->{{{f(x) = x^3 - 2=0^3-2=0-2=-2}}}
{{{1}}}|{{{-1}}} ->{{{f(x) = x^3 - 2=(1)^3-2=1-2=-1}}}
{{{2}}}|{{{6}}} ->{{{f(x) = x^3 - 2=2^3-2=8-2=6}}}

inverse 

{{{-2}}}|{{{0}}}
 {{{-1}}}|{{{1}}} 
{{{6}}}|{{{2}}} 




{{{drawing(600,600,-10,10,-10,10, 
circle(-2,0,.12),locate(-2,-0.5,p(-2,0)),
circle(-1,1,.12),locate(-1,1,p(-1,1)),
circle(6,2,.12),locate(6,2,p(6,2)),

circle(0,-2,.12),locate(0,-2,p(0,-2)),
circle(2,6,.12),locate(2,6,p(2,6)),
circle(1,-1,.12),locate(1,-1,p(1,-1)),
graph(600,600,-10,10,-10,10,11, x^3-2),
graph(600,600,-10,10,-10,10,(x+2)^(1/3)*sqrt(sin(7x))/sqrt(sin(7x) )),

red(locate(4,3,f^-1(x)=root(3,x+2))), green(locate(-3,-2,f(x)=x^3 - 2))   )}}}



domain of {{{f(x)}}}:

{{{R}}} (all real numbers)

interval notation:
({{{-infinity}}},{{{infinity}}})

range
{{{R}}} (all real numbers)

interval notation:
({{{-infinity}}},{{{infinity}}})


domain of {{{f^-1(x)}}}:

{ {{{x}}} element {{{R}}} : {{{x>=-2}}} }

interval notation:
[{{{-2}}},{{{infinity}}})

range:

{ {{{f(x)}}} element {{{R}}} : {{{f>=0}}} } (all non-negative real numbers)

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