If f : A → B and g : B → C are one-one functions, show that gof is a one-one function.


If f : A → B and g : B → C are one-one functions, show that gof is a one-one function.


Given,  f : A → B and g : B → C are one - one.
Then, gof : A → B
Let us take two elements x and y from A, such that

$(g o f)(x)=(g o f)(y)$

$\Rightarrow g(f(x))=g(f(y))$

$\Rightarrow f(x)=f(y)$ (As, $g$ is one-one)

$\Rightarrow x=y$ (As, $f$ is one-one)

Hence, gof is one-one.

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