Question 1003153
{{{ f(x)=sqrt( x^2+3x-4 ) * sqrt( 2-x-x^2 ) }}}

domain:
all {{{x}}} excluding the value that makes {{{  x^2+3x-4   }}} and {{{  2-x-x^2  }}}equal to zero

{{{  x^2+3x-4 =0  }}}
{{{  x^2-x+4x-4 =0  }}}
{{{  (x^2-x)+(4x-4) =0  }}}
{{{  x(x-1)+4(x-1) =0  }}}
{{{  (x+4)(x-1) =0  }}}
=>{{{x=1}}} or {{{x=-4}}}

{{{ 2-x-x^2 =0 }}}

{{{ 2-2x+x-x^2 =0 }}}
{{{ (2-2x)+(x-x^2) =0 }}}
{{{ 2(1-x)+x(1-x) =0 }}}
{{{ (2+x)(1-x) =0 }}}

=>{{{x=1}}} or {{{x=-2}}}

so, domain is:

{ {{{x}}} element {{{R}}} : {{{x = 1}}} }

range:

{ {{{y}}} element {{{R}}} : {{{y = 0}}} }

{{{ graph( 600, 600, -5, 5, -10, 60,-sqrt( x^2+3x-4 )( 2-x-x^2 ) ,sqrt( x^2+3x-4 )( 2-x-x^2 )) }}}

here is better graph that shows you imaginary and real part:


<a href="http://tinypic.com?ref=2a0ma2e" target="_blank"><img src="http://i66.tinypic.com/2a0ma2e.jpg" border="0" alt="Image and video hosting by TinyPic"></a>