Find the equivalent definition of `f(x)=max{x^2,(1-x)^2,2x(1-x)}`where `0lt=xlt=1`

Find the equivalent definition of f(x)=m a xdot{x^2,(-x)^2,2x(1-x)}where 0lt=xlt=1

The equivalent definition of f(x)=||x|-1| , is

Consider the function f(x)=max. [(x^(2) , (1-x)^(2) , 2x(1-x))] , x in [0,1] The interval in which f(x) is increasing, is

Let f(x) =M a xi mu m {x^2,(1-x)^2,2x(1-x)}, where 0lt=xlt=1. Determine the area of the region bounded by the curves y=f(x) ,x-axis ,x=0, and x=1.

Find the value of "cos"(2cos^(-1)x+sin^(-1)x) at x=1/5, where 0lt=pi and -pi/2lt=sin^(-1)xlt=pi/2dot

Discuss the applicability of Rolles theorem on the function f(x)={x^2+1,\ \ \ \ w h e n\ 0lt=xlt=1 3-x ,\ \ \ \ w h e n\ 1

Discuss the continuity of f(x)={(x{x}+1 ,, 0lt=x<1),(2-{x} ,, 1lt=x<2):} where {x} denotes the fractional part function.

Find f(x) when it is given by f(x)=max{x^(3),x^(2),(1)/(64)},AA x in [0, oo).

The domain of definition of f(x)=log_(1.7)((2-phi'(x))/(x+1))^(1//2) , where phi(x)=(x^(3))/(3)-(3)/(2)x^(2)-2x+(3)/(2) , is

f(x)={(4, xlt-1) ,(-4x,-1lt=xlt=0):} If f(x) is an even function in R then the definition of f(x) in (0,oo) is: (A) f(x)={(4x, 0ltxle1),(4, xgt1):} (B) f(x)={(4x, 0ltxle1),(-4, xgt1):} (C) f(x)={(4, 0ltxle1),(4x, xgt1):} (D) f(x)={(4, xlt-1),(-4x, -1lexle0):}