If $f:R\to R$ be defined by $f\left(x\right)=e^x$ and $g:R\to R$ be defined by $g\left(x\right)=x^2.$ The mapping gof : $R\to R$ be defined by $\left(gof\right)\left(x\right)$ $=g\left[f\right(x\left)\right]\forall x\in R.$ Then

Let $f\left(x\right)=\sin x+\cos ax$ be a periodic function. Then,

Let $f:X\to Y$ and $A, B$ are non-void subsets of $Y,$ then (where the symbols have their usual interpretation)