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If, f: A → B and g: B → C. Then which of the following statements are true: 1. f o g exists and it is a function on B. 2. g o f exists and it is function from A to C. 3. f o g does not exists. 4. g o f does not exists.

If, f: A → B and g: B → C. Then which of the following statements are true: 1. f o g exists and it is a function on B. 2. g o f exists and it is function from A to C. 3. f o g does not exists. 4. g o f does not exists. Correct Answer Only 2 and 3

Concept:

If, f: A → B and g: B → C. Then 

1. f o g (x) will exists only if: Co-domain of g = Domain of f. Then fog is a function from domain of g to co-domain of f.

2. g o f (x) will exists only if: Co-domain of f = Domain of g. Then gof is a function from domain of f to co-domain of g.

Calculation:

Here f: A → B and g: B → C.

The domain and co-domain of the function f is A and B respectively, whereas the domain and co-domain of the function g is B and C respectively.

As, we know fog (x) will exists only if: Co-domain of g = Domain of f, but here we can see that co-domain of g i.e C ≠ domain of f i.e A.

⇒ f o g does not exist.

As, we know g o f (x) will exists only if: Co-domain of f = Domain of g, here we can see that co-domain of f i.e B = domain of g i.e B.

⇒ g o f exists and it is a function from A to C.

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