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

If f(x)={{:(x",",0lexle1),(x+a",",xgt1):} then

If f(x)=x+4, g(x)=2x-1 and h(x) =3x then find (fog)oh .

If f(x)={{:(x^(3)(1-x)",",xle0),(xlog_(e)x+3x",",xgt0):} then which of the following is not true?

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

If f(x)=sin^(2)x, g(x)=sqrtx and h(x)=cos^(-1)x, 0 le xle 1, then

If f(x)={{:(2x-1,"when "xle0),(x^(2),"when "xgt0):},"then find "f((1)/(2)) and f((-1)/(2))

If f(x)={{:(x","" "xlt0),(1","" "x=0),(x^(2)","" "xgt0):}," then find " lim_(xto0) f(x)" if exists.

if f(x) = {{:(x+2",",xle-1),(cx^(2)",",xgt-1):}, then find c when lim(xto-1)f(x) exists.

f(x)={{:(x-1",", -1 le xle 0),(x^(2)",",0 lt x le 1):} and g(x)=sinx. Find h(x)=f(abs(g(x)))+abs(f(g(x))).

Let f(x) =e^(x-1)-ax^(2)+b and g(x)={{:(e^(x-1),xle1),(x^(2)+1,xgt1):}, then find the values of a and b such that f(x) xx g(x) is differentiable at x=1 .