Let `f(x)={(x+1",", x lt1),(2x+1",",1lt x le 2):}" and " g(x)={(x^(3)",", -1 le x lt 2),(x+2",",2 le x le 3):}`
find `fog(x)`.

Consider the functions f(x)={(x+1",",x le 1),(2x+1",",1lt x le 2):} and g(x)={(x^(2)",", -1 le x lt2),(x+2",",2le x le 3):} The range of the function f(g(x)) is

Let f(x)={{:(1+x",", 0 le x le 2),(3-x"," ,2 lt x le 3):} find (fof) (x).

Two functions are defined as under : f(x)={(x+1, x le 1), (2x+1, 1 < x le 2):} and g(x)={(x^2, -1 le x le 2), (x+2, 2 le x le 3):} Find fog and gof

If f(x) ={(x^(3)", " x lt1),(2x-1", " x ge 1):} " and " g(x)={(3x", " x le2),(x^(2)", " x gt 2):} " then find " (f-g)(x).

Consider two functions f(x)={([x]",",-2le x le -1),(|x|+1",",-1 lt x le 2):} and g(x)={([x]",",-pi le x lt 0),(sinx",",0le x le pi):} where [.] denotes the greatest integer function. The number of integral points in the range of g(f(x)) is

Consider two functions f(x)={([x]",",-2le x le -1),(|x|+1",",-1 lt x le 2):} and g(x)={([x]",",-pi le x lt 0),(sinx",",0le x le pi):} where [.] denotes the greatest integer function. The number of integral points in the range of g(f(x)) is

If f(x)={:{(3x^2+12x-1"," -1le x le2),(37-x ","2 lt x le 3):} then

Let f(x)={(2x+a",",x ge -1),(bx^(2)+3",",x lt -1):} and g(x)={(x+4",",0 le x le 4),(-3x-2",",-2 lt x lt 0):} If the domain of g(f(x))" is " [-1, 4], then

If f(x)={{:(,x^(2)+1,0 le x lt 1),(,-3x+5, 1 le x le 2):}

Let f(x)={(2x+a",",x ge -1),(bx^(2)+3",",x lt -1):} and g(x)={(x+4",",0 le x le 4),(-3x-2",",-2 lt x lt 0):} If a=2 and b=3, then the range of g(f(x)) is