# 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.

×