If `f(x)={[x] and x leq 0 and 1+[x] , x lt 0 and x in 1 then and x , x lt 0 and xin I` then

If function defined by f(x) ={(x-m)/(|x-m|) , x leq 0 and 2x^2+3ax+b , 0 lt x lt 1 and m^2x+b-2 , x leq 1 , is continuous and differentiable everywhere ,

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

If f(x) = {sinx , x lt 0 and cosx-|x-1| , x leq 0 then g(x) = f(|x|) is non-differentiable for

If f(x)={{:(x + 1, x gt 1),(0",", x=1 "then f'(0) equal to "),(7-3x"," , x lt 1):}

If f(x)={{:(x + 1, x gt 1),(0",", x=1 "then f'(0) equal to "),(7-3x"," , x lt 1):}

If f(x)={:{(1-x", for " 0 lt x le 1), ( 1/2 ", for " x=0):} , then in [0, 1]

f(x)={x+2, 0lt=x<2 and 6-x , xgeq2 and g(x)={1+tanx , 0 leq x lt pi/4 and 3-cotx , pi/4 leq x lt pi . find fog and discuss the continuity and differentiabillity of fog.

If f (x) = sin (2x ^(2) -2 [x]) for 0 lt x lt 1, then f ' ((sqrtpi)/(2))=