Let F and G be two real-valued function defined on R (the set of all real numbers)
F(x)=`{:{(,|x+1|,),(,x,):}`{:(,xle0,),(,xgt0,):}` G(x) =`{:{(,|x|+1,),(,-|x-2,):}`{:(,xle1,),(,xgt1,):}` and `H(x)=F(x)+G(x)`.
Point of discontinuity of H(x) are

Let F and G be two real-valued function defined on R (the set of all real numbers) F(x)={:{(,|x+1|,),(,x,):} {:(,xle0,),(,xgt0,):} G(x) ={:{(,|x|+1,),(,-|x-2,):} {:(,xle1,),(,xgt1,):} and H(x)=F(x)+G(x) . The value of definite integral int_(-2)^(2) H(x) dx is equal to

If f(x)={{:(x^(2),xle0),(x,xgt0):} and g(x)=-absx,x inR, then find fog .

If f(x)={{:(x^(2),xle0),(x,xgt0):} and g(x)=-absx,x inR, then find fog and gof.

If f(x)={(x^(2),xle1),(1-x,xgt1):} & composite function h(x)=|f(x)|+f(x+2) , then

If f(x)={(x^(2),xle1),(1-x,xgt1):} & composite function h(x)=|f(x)|+f(x+2) , then

Let f(x)={:{(x^(2)-1",",xle1),(-x^(2)-1",",xgt1.):} "Find"lim_(xrarr1)f(x).

If f(x)={{:(2x^(2)+1",",xle1),(4x^(3)-1",",xgt1):} , then int_(0)^(2)f(x)dx is

Let the function f, g, h are defined from the set of real numbers RR to RR such that f(x) = x^2-1, g(x) = sqrt(x^2+1), h(x) = {(0, if x lt 0), (x, if x gt= 0):}. Then h o (f o g)(x) is defined by