Answer
Yes, g is one-one
Work Step by Step
Given : $g:A\rightarrow B$ and $f:B\rightarrow C$, f and f o g are one-one
To prove: g is one-one
Proof:
Let us assume $$g(a)=g(b)$$
Let us take the function f of each side of the previous equation:$$f(g(a))=f(g(b))$$
Use definition of composition:$$(fog)(a)=(fog)(b)$$\
Since f o g is one-one:$$a=b$$
Thus, $g(a)=g(b)$, then implies $a=b$. By the definition of one-one , we have then proved that g is one-one.
