Find the domain of the function f(x)=2x2−x+1−1x+1−2x−1x3+1

f(x)=2x2−x+1−1x+1−2x−1x3+1 We must have 2x2−x+1−1x+1−2x−1x3+1≥0⇒ 2(x+1)−x2−x+1−(2x−1)(x+1)x2−x+1≥0⇒ −x2−x−2(x+1)x2−x+1≥0 ⇒−(x−2)(x+1)(x+1)x2−x+1≥0⇒2−xx2−x+1≥0, where x≠−1⇒ 2−x≥0,x≠−1  (as x2−x+1>0∀x∈R ) ⇒ x≤2,x≠−1 Hence, domain of the function is (−∞,−1)∪(−1,2] .