For every integer n, let an and bn be real numbers. Let function f: R→R be given by f(x)={an+sinπx, for x∈[2n,2n+1]bn+cosπx, for x∈(2n−1,2n) , for all integers n.If f is continuous, then which of the following hold(s) for all n?

For every integer n, let an and bn be real numbers. Let function f: R�

1.	For every integer n, let an and bn be real numbers. Let function f: R→R be given by f(x)={an+sinπx, for x∈[2n,2n+1]bn+cosπx, for x∈(2n−1,2n) , for all integers n.If f is continuous, then which of the following hold(s) for all n?
Answer» For every integer $n,$ let $a_{n}$ and $b_{n}$ be real numbers. Let function $f : R \to R$ be given by $f (x) = {\begin{matrix} a_{n} + sin π x, for x \in [2 n, 2 n + 1] b_{n} + cos π x, for x \in (2 n - 1, 2 n) \end{matrix}$ , for all integers $n .$ If $f$ is continuous, then which of the following hold(s) for all $n ?$