Let `f(x)={x^2 ; 0 lt x lt 2 and 2x-3 ; 2 leq x lt 3 and x+2 ; x leq 3 ` then

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

Let f (x)= {{:(x ^(2),0lt x lt2),(2x-3, 2 le x lt3),(x+2, x ge3):} then the tuue equations:

Let f (x)= {{:(x ^(2),0lt x lt2),(2x-3, 2 le x lt3),(x+2, x ge3):} then the tuue equations:

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

Let f(x) = {{:(x^(2) - 1, 0 lt x lt 2),(2x + 3, 2 le x lt 3):} , the quadratic equation whose roots are lim_(x rarr 2^(-)) f(x) and lim_(x rarr 2^(+)) f(x) is :

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

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