Conjecture: If $g(x)$ is injective, and $g(f(x))$ is injective, then $f(x)$ is injective
How can I prove that conjecture formally?
Thanks!
Conjecture: If $g(x)$ is injective, and $g(f(x))$ is injective, then $f(x)$ is injective
How can I prove that conjecture formally?
Thanks!
Let $f(a)=f(b)$. Hence $g(f(a))=g(f(b))$. Since $gf$ is injective. Therefore $a=b$