Find the range and domain : f(x) = ( x2 - 3x+ 2 ) / ( x2 + x - 6 )

The given function is;
fx=x2-3x+2x2+x-6For domain of fx:Clearly, fx is defined for all real values of x except the values of the values of x for which x2+x-6=0i.e. x2+3x-2x-6=0 i.e. x+3x-2=0, i.e. x=-3 or x=2.Therefore domain of fx is R--3,2.
For range of f(x):
let  y=fx.Then,fx=y=x2-3x+2x2+x-6yx2+x-6=x2-3x+2y-1x2+y+3x-23y+1=0x=-y+3±y+32+8y-13y+12y-1x=-y+3±25y2-10y+12y-1=-y+3±5y-122y-1x=-y+3±5y-12y-1x=2, -3y+1y-1x=-3y+1y-1,      As x2Clearly, x takes all real values if y-10 i.e. y1Hence, range of fx is R-1

  • -17
solving it,     f(x) = x2 - 3x +2  / x2 + x -6 
                          = (x-1) ( x-2) / (x-1) (x-3)  = (x-2) / (x-3)
                        =  so, x+3 ≠ 0   so x ≠ -3
                    so, domain R - { -3}
range isR
 
Hope it helps !!!
 
  • -6
why 2 is omitted while finding domain??? 
 
  • -2
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