Let ` f(x) = x^3-x^2 + x + 1 and g(x) = [max{f(t):0<=x<=x}, 0<=x<=1 and 3-x, 1

Let f(x) = -x^(3) + x^(2) - x + 1 and g(x) = {{:(min(f(t))",",0 le t le x and 0 le x le 1),(x - 1",",1 lt x le 2):} Then, the value of lim_(x rarr 1) g(g(x)) , is........ .

Let f(x) = x^(2) + 2x +5 and g(x) = x^(3) - 1 be two real functions. Find (f+g)(x), (f-g)(x), (fg)(x) and ((f)/(g))(x) .

Let f(x)=x^(3)-x^(2)+x+1 and g(x) be a function defined by g(x)={{:(,"Max"{f(t):0le t le x},0 le x le 1),(,3-x,1 le x le 2):} Then, g(x) is

Let f(x)=|x-1|+|x-2| and g(x)={min{f(t):0<=t<=x,0<=x<=3 and x-2,x then g(x) is not differentiable at

Let f(x)=sin x and cg(x)={max{f(t),0 pi Then ,g(x) is

Let F(x) = f(x) +g(x) , G(x) = f(x) - g( x) and H(x) =(f( x))/( g(x)) where f(x) = 1- 2 sin ^(2) x and g(x) =cos (2x) AA f: R to [-1,1] and g, R to [-1,1] Now answer the following If the solution of F(x) -G (x) =0 are x_1,x_2, x_3 --------- x_n Where x in [0,5 pi] then

Let f(x)=||x|-1|-1| and g(x)-(max f(t):x<=t<=x+1,x in R} The graph of g(x) is symmetrical about