Question 1179039
{{{f(x) = (x - 5)^2}}}

table

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


{{{4}}}|{{{1}}} ->{{{f(x) = (4 - 5)^2=1}}}
{{{3}}}|{{{4}}} ->{{{f(x) = (3 - 5)^2=4}}}
{{{2}}}|{{{9}}} ->{{{f(x) = (2 - 5)^2=9}}}

inverse 

reverse {{{x}}} and {{{y}}}

{{{1}}}|{{{4}}}
 {{{4}}}|{{{3}}} 
{{{9}}}|{{{2}}} 

{{{drawing(600,600,-10,10,-10,10, 
circle(4,1,.12),locate(4,1,p(4,1)),
circle(3,4,.12),locate(3,4,p(3,4)),
circle(2,9,.12),locate(2,9,p(2,9)),

circle(1,4,.12),locate(1,4,p(1,4)),
circle(4,3,.12),locate(4,3,p(4,3)),
circle(9,2,.12),locate(9,2,p(9,2)),
graph(600,600,-10,10,-10,10,11, (x - 5)^2),
graph(600,600,-10,10,-10,10,(5+sqrt(x))*sqrt(sin(7x))/sqrt(sin(7x) )),
graph(600,600,-10,10,-10,10,(5-sqrt(x))*sqrt(sin(7x))/sqrt(sin(7x) )),

red(locate(5,6,f^-1(x)=5 +- sqrt(x))), green(locate(3,-2,f(x)=(x - 5)^2))   )}}}



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

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

interval notation:

({{{-infinity}}},{{{infinity}}})


range:

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

[{{{0}}},{{{infinity}}})



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

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

[{{{0}}},{{{infinity}}})


range:

{ {{{f}}} element {{{R}}} : {{{y>=5}}} }

[{{{5}}},{{{infinity}}})