[" 4.Show that the function "f:R rarr|x in R:-1<],[" defined by "f(x)=1.1x|" ,"x in R" is one one and onto."]

Show that the function f : R rarr {x in R : -1 < x < 1} defined by f(x) = x/(|x|), x in R is one-one function.

Show that the function f : R rarr { x in R : -1 lt x lt 1} defined by f (x) = (x)/(1+|x|), x in R is one - one and onto function.

Show that the function f : R rarr {x inR:-1lt x lt1} defined by f(x) =x/(1+|x|),x in R is one one and onto function.

Show that function f:R rarr{x in R:-1

Show that the function f:R rarr R:f(x)={1 if x is rational and -1, if x is irrational is many- one into

Show that the function f: R rarr R defined by f(x) = (3x-1)/2, x in R is one-one and onto function.

Show that the function f:R rarr R given by f(x)=cos x function f:R, is neither one-one nor onto.

Show that the function f:R rarr R given by f(x)=x^(3)+x is a bijection.

Show that the function f:R rarr R given by is injective.