Find the equivalent definition of `f(x)=m a xdot{x^2,(-x)^2,2x(1-x)}w h r e0lt=xlt=1`

Explanation

Let us consider `f_(1)(x) = x^(2), f_2(x) = (1-x)^(2) and f_(3)(x) =2x (1-x)`
Now taking graph for `f_1(x), f_2(x) and f_3(x)`,

Since we want to find the maximum of three function `f_1(x) , f_2(x) and f_3(x)` :
`" "f(x) ={{:((1-x)^(2)",",, 0le x lt (1)/(3)), (2x(1-x)",",, (1)/(3) le x lt (2)/(3)","), (x^(2)",",, (2)/(3) le x le 1):}`