Composition of function: Conditions and Properties - Practice Questions & MCQ

Let $\mathrm{f}: \mathrm{A} \rightarrow \mathrm{B}$ and $\mathrm{g}: \mathrm{B} \rightarrow \mathrm{C}$ be two functions. Then the composition of f and g is denoted by gof and defined as the function gof : $\mathrm{A} \rightarrow \mathrm{C}$ given by $\operatorname{gof}(x)=g(f(x))$

Properties of composition:

In general fog $\neq$ gof (Not commutative)
$\mathrm{fo}(\mathrm{goh})=(\mathrm{fog})$ oh $\quad$ (Associative $)$
If $f$ and $g$ are bijections then fog and gof are also bijections

The composition of any function with the identity function is the function itself. If $f: A \rightarrow B$, then $f o I_A=I_B o f=f$