Question

Question: If f and$\mathit{f}\mathbf{\circ }\mathit{g}$ are onto, does it follow that g is onto? Justify your answer.

Short answer

Answer:

No, it doesn’t follow that g is onto.

Step-by-step solution

Step: 1

For example, suppose that $A\left\{a\right\},B=\{b,c\}$, and$C=\left\{d\right\}$ .

Step: 2

Let $g\left(a\right)=b,f\left(b\right)=d$,and$f\left(c\right)=d$ .

Then f and$f\circ g$ are onto, but is not