The domain of the function f(x)=x−1−x2 is
−1,−12∪12,1
[-1, 1]
−∞,−12∪12,+∞
12,1
For f (x) to be defined, we must havex−1−x2≥0 or x≥1−x2>0∴x2≥1−x2 or x2≥12 Also, 1−x2≥0 or x2≤1 Now, x2≥12⇒x−12x+12≥0 ⇒x≤−12 or x≥12 Also, x2≤1⇒(x−1)(x+1)≤0⇒−1≤x≤1 Thus, x>0,x2≥12 and x2≤1⇒x∈12,1