Question 830767
if you mean this

{{{ f(x)= (x+3)^(3/2) }}}, then you have


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


{{{f(x)=sqrt((x+3)^2(x+3))}}}


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

solutions:

{{{ (x+3)sqrt((x+3))=0}}}

if {{{ (x+3)=0}}}=> {{{x=-3}}}............one real root

domain:

{ {{{x}}} element {{{R}}} : {{{x>=-3}}} }

range:

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

here is the graph:

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