Question

How does the frequency of f(x) = cos(2x) relate to the frequency of the parent function cos x?

Answer 1

Answer:

The frequency of f(x) is two times the frequency of the parent function.

Step-by-step explanation:

We can say that the number that is beside the x is equal to $2\pi *f$, where f is the frequency.

Then, for the parent function, we get:

$1 = 2\pi f_1$

or solving for $f_1$:

$f_1=\frac{1}{2\pi }$

At the same way, for f(x), we get:

$2=2\pi f_2\\f_2=2(\frac{1}{2\pi })$

But $\frac{1}{2\pi }$ is equal to $f_1$, so we can write the last equation as:

$f_2=2f_1$

It means that the frequency of f(x) is two times the frequency of the parent function.