Question

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

पर्याय

• f ^–1 o g^–1

• f o g

• g^–1 o f^–1

• g o f

Answer 1

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 I_B o f)  .......(Where I_B is identity function on B)

= (f ^–1 o I_B) o f

= f ^–1 o f

= I_A

Thus (g o f)^–1 = f ^–1 o g ^–1