If `f(x)={x^2sin(pix)/2,|x|<1x|x|,|x|geq1,t h e nf(x)i s` an even function (b) an odd function a periodic function (d) none of these

If f(x)={x^2 sin((pi x)/2), |x| =1 then f(x) is

If f(x)={("sin"(pix)/2,, x lt1),(4x-3,,1lexle2),(log2(2x^(2)-4),,2ltxlt3):} then value of lim_(xto1)f(x)+lim_(xto2^(+))f(x) is

A function f(x) given by f(x)={{:(x^(2)sin""(pix)/(2), |x| lt1),(x|x|,|x| ge1):}is

Let f(x)={{:(x^(2) sin ((pix)/(2)),-1 lt x lt 1, x ne 0),(x|x|, x gt 1 or x le -1):} . Then ,

If f(x) = {{:("sin"(pix)/(2)",",x lt 1),([x]",",x ge 1):} , where [x] denotes the greatest integer function, then

If f(x)={sin((a-x)/2)t a n[(pix)/(2a)] for x > a and ([cos((pix)/(2a))])/(a-x) for x < a, then a. f(a^-)<0 b. f has a removable discontinuity at x=a c. f has an irremovable discontinuity at x=a d. f(a^+)<0

The number of values of x , x ∈ [-2,3] where f (x) =[x ^(2)] sin (pix) is discontinous is (where [.] denotes greatest integer function)

Which of the following functions from A={x in R :-1lt=xlt=1} to itself are bijections? f(x)=|x| (b) f(x)=sin((pix)/2) (c) f(x)=sin((pix)/4) (d) none of these

The left hand derivative of f(x)=[x]sin(pix) at x = k , k in Z , is

The period of f(x)=sin""(2pix)/(3)+ cos""(pix)/(2) , is