JEE MAIN - Mathematics (2021 - 25th July Evening Shift - No. 13)
Consider function f : A $$\to$$ B and g : B $$\to$$ C (A, B, C $$ \subseteq $$ R) such that (gof)$$-$$1 exists, then :
f and g both are one-one
f and g both are onto
f is one-one and g is onto
f is onto and g is one-one
Explanation
$$\therefore$$ (gof)$$-$$1 exist $$\Rightarrow$$ gof is bijective
$$\Rightarrow$$ 'f' must be one-one and 'g' must be ONTO.
$$\Rightarrow$$ 'f' must be one-one and 'g' must be ONTO.
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