Question

If f and$\mathrm{f}\circ \mathrm{g}$ are one-to-one, does it follow that g is one-to-one? Justify your answer.

Short answer

If$f\circ g$ and are one-to-one, it follow that g is one-to-one. Hence, the result is yes.

Step-by-step solution

Step: 1

For example, suppose that $A=\left\{a\right\}$,role="math" localid="1668421884405" $\mathrm{B}=\{b,\mathrm{c}\}$ and $\mathrm{C}=\left\{d\right\}$.

Step: 2

Let $g\left(a\right)=a$, role="math" localid="1668421945217" $f\left(b\right)=b$ and $f\left(c\right)=d$. Then f and$f\circ g$ are one, and g is one-to-one.