If fx1−fx2=fx1−x21−x1x2 for x1, x2 ∈ [–1, 1], then f (x) is

When x1 = –1 and x2 = 1, then f(−1)−f(1)=f−1−11+1(1)=f(−1)⇒ f (1) = 0,which is satisfied when f(x)=tan−1⁡1−x1+xWhen x1 = x2 = 0, thenf(0)−f(0)=f0−01−0=f(0)⇒f(0)=0When x1 = –1 and x2 = 0, thenf(−1)−f(0)=f−1−01−0=f(−1)⇒f(0)=0which is satisfied when f(x)=log⁡1−x1+x and, f(x)=log⁡1+x1−xThe correct option is (1), (2) and (3)