Assertion(A): A function $f$ satisfies the condition

 $f(x+T)=$$1+{\left\{1-3f\left(x\right)+3{\left(f\right(x\left)\right)}^2-{\left(f\right(x\left)\right)}^3\right\}}^{\frac{1}{3}}$  

( Where T is a fixed positive number) is periodic with period 2T.
 

Reason(R): If $f(x+2T)=f\left(x\right)$  , then period of $f\left(x\right)$ is 2T. 
 

$f(x+T)=1+{\left\{1-3f\left(x\right)+3{\left(f\right(x\left)\right)}^2-{\left(f\right(x\left)\right)}^3\right\}}^{1/3}$

$=1+{\left\{{\left(1-f\left(x\right)\right)}^3\right\}}^{1/3}$

$f\left(x-T\right)=-f\left(x\right)+2$     …(i)

$\Rightarrow f(x+T)+f\left(x\right)=2$    …(ii)

$\therefore f(x+2T)+f(x+T)=2$

$\therefore$  from (ii)-(i) we get

$f\left(x+2T\right)-f\left(x\right)=0$$\Rightarrow f(x+2T)=f\left(x\right)$

$\Rightarrow$Period of $f\left(x\right)$   is 2T
Assertion (A) & Reason (R) both are true & Reason (R) is correct explanation of Assertion (A).