Let $n$ be an odd natural number , to find a continuous real valued function on $\mathbb R$ which takes every value exactly $n$ times Let $n$ be an odd natural number . We know $\mathbb R = \cup_{k \in \mathbb Z} [nk\pi , n(k+1)\pi]$ . So for every $k \in \mathbb Z$ , define 
$h(x):=2k+1-(-1)^k \cos x , \forall x \in [nk\pi , n(k+1)\pi ]$ , then does the function $h : \mathbb R \to \mathbb R$ , takes 
every value exactly $n$ times ? Can someone please provide any other continuous function(s) on $\mathbb R$ which takes every value exactly $n$ times for odd $n$ ? Please help . Thanks in advance . 

Yes, your function appears to meet the requirements.  Here is a sketch for $n=5$

Another approach without the need for intervals might be to take a sinusoidal curve and add a linear element to shift successive peaks and troughs up, perhaps something like 
$$f(x)= \frac{2}{n\pi}x +\cos(x)$$
which for $n=5$ looks like 

