`f(x)={3-x^2 ; x leq -2 and ax+b ; -2 lt x lt 2 and x^2/2 ; x leq 2`

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)) .

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) is continuous at x=2 and x=10 , where f(x)={:{(5", if " x le 2),(ax+b", if " 2 lt x lt 10),(21", if " x ge 10):} , then

If f(x) ={ x^2-1, 0 lt x lt 2 , 2x+3 , 2 le x lt 3 then the quadratic equation whose roots are lim_(x->2^+)f(x) and lim_(x->2^-)f(x) is

f(x)={{:(|x|+3, if x le -3),(-2x, if -3 lt x lt 3 ),(6x + 2, if x ge3):}

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

Consider the function f(x) =[(1-x,0 leq x leq 1),(x+ 2, 1 lt x lt 2),(4-x,2 leqxleq4)). Let lim_(x->1) f(f(x))= l and lim_(x->1) f(f(x))=m then which one of the following hold good ? (A) l exist but m does not (B) m exist but l does not (C) both exist (D) both does not exist

Find the values of a and b such that the function defined by is continuous. f(x) = {(x^(2)+1","," "xle 2),(ax + b",", 2 lt x lt 10),(2x+1",", " "x ge 10):}