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.

A,B,E B only A,B,C A,B

1 solution

Madhav Gupta
Oct 21, 2015

c d e will not be periodic as 1st function has period=pi= irrational and second= 1 =rational hence after taking lcm the period will not exist...
a-fogx=sin^2({x}) as {X} repeats in (0,1) hence output repeats in interval of 1 so fundamental period=pi but period =1,2,3...
b-gofx={sin^2(X)} as output has {} operator so output repeats itself in 0,pi [ as the is square on sin] hence the output outside {} repeats at (0,pi)

Do you know its property? 10

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