Question

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

Short answer

Answer:

If f and $f\circ g$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 ,$A=\left\{a\right\},B=\left\{b,c\right\}andC=\left\{d\right\}$.

Step: 2

Let $\text{g(a)=a,f(b)=band(c)=d}$. Then f and are one, $f\circ g$and g is one-to-one.