Question

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

Short answer

No, it doesn’t follow that g is onto.

Step-by-step solution

Step: 1

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

Step: 2

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

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