Question 1196095

 

{{{f(x)=sqrt(2x^2-3x-20)}}}


The domain of a radical function is any x value for which the radicand (the value under the radical sign) is not negative.



will be all values of {{{x}}} that make {{{2x^2-3x-20>= 0}}}

{{{2x^2-3x-20>= 0 }}} factor   

{{{(x - 4) (2x + 5)>= 0}}}


solutions

{{{(x - 4)  >= 0}}}  if {{{ x >=4}}}

or

{{{2x + 5>= 0 }}} if  {{{x >=-5/2}}}


so domain is

{  {{{x }}} element {{{ R}}} : {{{x<=-5/2}}} or{{{ x>=4}}} }