Concept:A function f is even if f(−x)=f(x) and odd if f(−x)=−f(x) for all x in its domain.Explanation:We are given f(x)=ln(x2+1−x).First, find f(−x):f(−x)=ln((−x)2+1−(−x))=ln(x2+1+x).Now compute −f(x):−f(x)=−ln(x2+1−x)=ln((x2+1−x)−1).Simplify the reciprocal by rationalizing:x2+1−x1=(x2+1−x)(x2+1+x)x2+1+x=(x2+1)−x2x2+1+x=x2+1+x.Thus −f(x)=ln(x2+1+x).Comparing, f(−x)=ln(x2+1+x)=−f(x).Hence f satisfies the condition for an odd function.Answer:The function f is an odd function. Therefore, the correct option is B.