The value of the function f(x)=x2−3x+2x2+x−6 lies in the interval

f (x) is defined if x2 + x – 6 ≠ 0i.e., (x + 3) (x – 2) ≠ 0 i.e. x ≠ – 3, 2∴ Domain (f)=(−∞,∞)\{−3,2}Let y=x2−3x+2x2+x−6 ⇒x2y+xy−6y=x2−3x+2⇒x2(y−1)+x(y+3)−(6y+2)=0For x to be real, (y + 3)2 + 4 (y – 1) (6y + 2) ≥ 0⇒ 25y2 – 10y + 1 ≥ 0 i.e. (5y – 1)2 ≥ 0which is true for all real y.∴ Range of f = (–∞, ∞).