Question

Which of the following is true for the function f(x)=2cos(x2)

a. The period is π


b. The period is π2


c. The period is 2π

d. The period is 4π

e. The period is 2

Answer 1

c. The period is 2π

Explanation:

The period of a function is the smallest value of $p$ for which
`f(x+p) = f(x)` for all x.

For the function f(x) = 2cos(x^2), we can see that f(x+2π) = f(x) for all x.

This is because the cosine function has a period of 2π. Therefore, the period of f(x) = 2cos(x^2) is
`\boxed{2\pi}`