If `f(x) = x^2 -2|x|`, then test the continuity and differentiability of `g(x)` in the interval `[-2,3]`,where `g(x)=min {f(t) : 2 leq t leq x} ,-2 leq x lt 0 and max {f(t) : 0leq t leq x,0 leq x leq 3`.

F(x)=x^(3)-3x^(2)+6 and g(x)=max{F(t):x+1 =0 Find continuity and differentiability of g(x) for x in[-3,1]

Let f(x)=1+x , 0 leq x leq 2 and f(x)=3−x , 2 lt x leq 3 . Find f(f(x)) .

Let f (x) = x^3-x^2-x+1 and g(x) = {max{f(t); 0<=t<=x}, 0<=x<=1, 3-x, 1<=x<=2 Discuss the continuity and differentiability of the function g (x) in the interval (0, 2).

Let f(x)=x^(3)-x^(2)-x+1 and g(x)={max{f(t);0<=t<=x},0<=x<=1,3-x,1<=x<=2 Discuss the continuity and differentiability of the function g(x) in the interval (0,2).

Make a rough sketch of the region given below and find its area using integration {(x,y): 0 leq y leq x^2+3,0 leq y leq 2x+3,0 leq x leq 3} .

Let f(x)=f_1(x)-2f_2 (x), where ,where f_1(x)={((min{x^2,|x|},|x|le 1),(max{x^2,|x|},|x| le 1)) and f_2(x)={((min{x^2,|x|},|x| lt 1),({x^2,|x|},|x| le 1)) and let g(x)={ ((min{f(t):-3letlex,-3 le x le 0}),(max{f(t):0 le t le x,0 le x le 3})) for -3 le x le -1 the range of g(x) is