If `f:RR rarr RR` is defined by `f(x)=x-[x] -(1)/(2)" for "x in RR`, where `[x]` is the greatest integer not exceeding x, then `{x in RR : f(x)=(1)/(2)}=`

If f:RR rarr RR is defined by f(x)=[(x)/(2)] for x in RR , where [y] denotes the greatest integer not exceeding, y then {f(x):|x| lt 71}=

If f:RR to RR is a function defined by f(x)=[x]cos((2x-1)/(2))pi , where [x] denotes the greatest integer function, then f is-

If RR rarrC is defined by f(x)=e^(2ix)" for x in RR then, f is (where C denotes the set of all complex numbers)

Let f: RR to RR be a function defined by f(x)={{:([x],x le2),(0,x gt2):} , where [x] is the greatest integer less than or equal to x. If I=int_(-1)^(2)(xf(x^(2)))/(2+f(x+1))dx , then the value of (4I-1) is-

Prove that the mapping f: RR rarr RR defined by , f(x)=x^(2)+1 for all x in RR is neither one-one nor onto.

Prove that the greatest integer function f: RR rarr RR , given by f(x)=[x] , is neither one-one nor onto, where [x] denotes the greatest integer less than or equal to x.

Prove that the greatest integer function f: RR rarr RR , given by f(x)=[x] , is neither one-one nor onto, where [x] denotes the greatest integer less than or equal to x.

Prove that the function f: RR rarr RR defined by, f(x)=sin x , for all x in RR is neither one -one nor onto.

The function f : RR to RR is defined by f(x) = sin x + cos x is