If `f:RR rarr RR,` then `f(x)= |x|` is

Show that the modulus function f: RR rarr RR , given by f(x)=|x| is neither one-one nor onto Where |x|={(x " when "x ge 0),(-x " when " x lt 0):}

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.

The largest domain on which the function f: RR rarr RR defined by f(x)=x^(2) is ___

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}=

Show that the signum function f:RR rarr RR , given by f(x)={(1" if "x gt 0),(0 " if "x = 0),(-1 " if " x lt0):} is neither one-one nor onto.

If f: RR rarr RR, f(x) = {(1,; "when" x in QQ), (-1,;"when" x notin QQ):} then image set of RR under f is

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.

function f and g are defined as follows: f:RR-{1} rarr RR, where f(x) =(x^(2)-1)/(x-1) and g: RR rarr RR g(x)=x+1, RR being the set of real numbers .Is f=g ? Give reasons for your answer.