Which of the following functions is non-periodic, here [.] and {.} denotes the greatest integer function and fractional part respectively?

$\frac{2^x}{2^{[x]}}$ $\sin^{-1}(\{x\})$ $\sin^{-1}(\sqrt{x})$ $\sin^{-1}(\cos(x^2))$

$\sin^{-1}(\cos(x^2))$

Period of $\frac{2^x}{2^{[x]}}$ is 1. Period of $\sin^{-1}\{x\}$ is 1. Period of $\sin^{-1}(\sqrt{x})$ is 2π where as $\sin^{-1}(\cos x^2)$ is non−periodic.