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  4. Let A and B be non empty sets in R and f: A → B is a bijective function. Statement 1: f is an onto function. Statement 2: There exists a function g: B → A such that fog = IB.

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Q. Let A and B be non empty sets in R and f : $A \to B$ is a bijective function.
Statement 1 : f is an onto function.
Statement 2 : There exists a function g : $B \to A$ such that fog = $I_B$.

AIEEEAIEEE 2012Relations and Functions - Part 2

Solution:

Let A and B be non-empty sets in R.
Let f : $A \to B$ is bijective function.
Clearly statement - 1 is true which says that f is an onto function.
Statement - 2 is also true statement but it is not the correct explanation for statement-1