The correct option is B R
Given denominator
2x2−2x+1
=2[x2−x]+1
=2[x2−x+14−14]+1
=2[(x−12)2]+12≥0 ∀x∈R
Now for f(x) to be defined
x4−2x3+3x2−2x+2≥0
⇒(x4+3x2+2)−(2x3+2x)≥0
⇒(x2+1)(x2+2)−2x(x2+1)≥0
⇒(x2+1)(x2−2x+2)≥0
⇒(x2+1)((x−1)2+1)≥0,⇒x∈R
Hence, Domain is R