Proving a function is periodic??? (1 Viewer)

[xwrathbringerx]

The function f with domain R (all real numbers) is defined by f(x) = e^[cos(x)]. Prove that f is periodic and state its period.

I've always had trouble with graphs. Could someone please explain to me how this particular type of question works again?

Thanxx!

 

[Drongoski]

The function f with domain R (all real numbers) is defined by f(x) = e^[cos(x)]. Prove that f is periodic and state its period.

I've always had trouble with graphs. Could someone please explain to me how this particular type of question works again?

Thanxx!

A function f(x) is said to be periodic if :

f(x + p) = f(x) (p nonzero)
and p is the period of this function if it is the smallest such p

Thus: f(x) = e^cos(x)

Then: f(x + 2pi) = e^cos(x+2pi) = e^cos(x) = f(x)
and 2 pi is the smallest such 'p' (same as for g(x) = cos(x) )

.: f(x) is periodic with period 2 pi