If `f(x)={3, x lt o and 2x+1, x leq 0` then

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

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 ,

If f(x)=sgn(x-2) xx [In x], 1leq x leq 3 and {x^2} ,-3 lt x leq 3.5 where [.] denotes the greatest integer function and {.} represents the fractional part functon, then the number of points of discontinuity in [1,3.5] is

Let f_1(x)={x, x leq x leq 1 and 1 x gt1 and 0 ,otherwise f_2(x) =f_1 (-x) for all x abd f_3(x)=-f_2(x) for all x and f_4(x)=-f_3(-x) for all x Which of the following is necessarily true?

Let f_1(x)={x, x leq x leq 1 and 1 x gt1 and 0 ,otherwise f_2(x) =f_1 (-x) for all x abd f_3(x)=-f_2(x) for all x and f_4(x)=-f_3(-x) for all x Which of the following is necessarily true?

If f(x)={{:(,1,x lt 0),(,1+sin x,0 le x lt (pi)/(2)):} then derivative of f(x) x=0

If f(x)={{:(,1,x lt 0),(,1+sin x,0 le x lt (pi)/(2)):} then derivative of f(x) at x=0

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.

A function defined by f(x)=x+a for x lt 0; x for 0 leq x lt 1; b-x for x geq 1 is continuous in [-2,2]. Show that (a+b) is even