If `f(x)={(3x^2+12x-1,-1lexle2),(37-x,2ltxle3):}`

If f(x)={(x[x], 0lexlt2),((x-1)[x],2lexle3):} , then f(x) is

Two functions are defined as under, f(x)={(x+1, x le1),(2x+1, 1ltxle2):} g(x)={(x^2, -1lexlt2),(x+2, 2lexle3):} Find fog and gof

If f(x)={(x[x], 0lexlt2),((x-1)[x], 2lexle3'):} , where [.] denotes the greatest integer function, then

Let f(x)={(x+2,-1lexle0),(1,x=0),(x/2,0ltxle1):} Then on [-1,1] this function has

The number of points of discontinuity of g(x)=f(f(x)) where f(x) is defined as, f(x)={1+x ,0lexle2 3-x ,2ltxle 3

Consider two function y=f(x) and y=g(x) defined as f(x)={{:(ax^(2)+b,,0lexle1),(bx+2b,,1ltxle3),((a-1)x+2c-3,,3ltxle4):} and" "g(x)={{:(cx+d,,0lexle2),(ax+3-c,,2ltxle3),(x^(2)+b+1,,3ltxle4):} underset(xrarr2)(lim)(f(x))/(|g(x)|+1) exists and f is differentiable at x = 1. The value of limit will be

f(x)={(x-1, -1lexlt0),(x^2, 0ltxle1):} and g(x)=sin x. Then find h(x)=f(|g(x)|)+|f(g(x))|

If the function . g(x)={(ksqrt(x+1),0lexle3),(mx+2,3ltxle5):} is differentiable, then the value of k+m is

Let f(x) be defined on [-2,2] and is given by f(x)={(-1, -2lexlt0),(x-1, 0lexle2):} and g(x)=f(|x|)+|f(x)|, then find g(x).

If f(x)={(-x-pi/2, x le -pi/2),(-cosx, -pi/2ltxle0),(x-1, 0ltcle1),(lnx, x gt 1):}