Let f: A → B and g: B → C be the bijective functions. Then (g o f)–1 is ______.

Question

KollegeApply · Accepted Answer

Let f: A → B and g: B → C be the bijective functions. Then (g o f)–1 is f –1 o g–1. Explanation: Given that, f: A → B and g: B → C be the bijective functions. (f –1 o g–1) o (g o f) = f –1 o (g–1 o g o f) = f –1 o (g–1 o g) o f ......(As composition of functions is associative) = f –1 o IB o f) .......(Where IB is identity function on B) = (f –1 o IB) o f = f –1 o f = IA Thus (g o f)–1 = f –1 o g –1

AChoose Your Answer