Find the range and domain : f(x) = ( x2 - 3x+ 2 ) / ( x2 + x - 6 ) Share with your friends Share 7 Tanveer Sofi answered this 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-6⇒yx2+x-6=x2-3x+2⇒y-1x2+y+3x-23y+1=0⇒x=-y+3±y+32+8y-13y+12y-1⇒x=-y+3±25y2-10y+12y-1=-y+3±5y-122y-1⇒x=-y+3±5y-12y-1⇒x=2, -3y+1y-1⇒x=-3y+1y-1, As x≠2Clearly, x takes all real values if y-1≠0 i.e. y≠1Hence, range of fx is R-1 -15 View Full Answer Shikhar Dutta answered this 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 !!! -10 Tamanna Choudhury answered this why 2 is omitted while finding domain??? -4
