`1:y=log_a[x^1001 -x^101 +x-1]` is an onto function in `R->R.`

Show that the function f : R to R {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 to R {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 to R {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 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->{x in R :-1ltxlt1} defined by f(x)=x/(1+|x|),x in R is one-one and onto function.

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 : Rrarr {x in R : – 1 < x < 1} defined by f(x)=x/(1+|x|), x in R is one one and onto function.

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

Statement-1 : f : R rarr R, f(x) = x^(2) log(|x| + 1) is an into function. and Statement-2 : f(x) = x^(2) log(|x|+1) is a continuous even function.