# Do you know its property? 10

**Geometry**Level 5

If \(f(x)=\sin^2x\) and \(g(x)=\{ x \}\) are real-valued functions, then which of the followings are true :

A. Period of \(f[g(x)]\) will be \(2\).

B. Fundamental Period of \(g[f(x)]\) will be \(\pi\).

C. Period of \(f[g(x)]+g[f(x)]\) will be \(\pi\).

D. Period of \(f[g(x)]+g[f(x)]\) will be \(1\).

E. \(f[g(x)]+g[f(x)]\) is periodic. But its fundamental period is not defined.

**Details:** \(\{..\}\) denotes Fractional Function.