# If y=f(x) has a period of 6, what is the period of y=f(1/2x)?

Nov 9, 2016

12

#### Explanation:

If f(x+P) = f(x) and P is least and > 0, P is called the period of f(x).

Let F(x) = f(kx). Then,

F(x+P/k) = f(k(x+P/k))=f(kx+P)=f(kx)=F(x).

So, the period of F(x)=f(kx) is P/k.

Here, P/k=(6)/(1/2)=12.