Help me please

X,Y - topological spaces, $\displaystyle a\in X, b\in Y$

Prove that following functions are continuous:

1.$\displaystyle f:X\rightarrow X\times Y, f(x)=(x,b)\: \forall x \in X$

2.$\displaystyle g:Y\rightarrow X\times Y, g(y)=(a,y)\: \forall y \in Y$