Show that the Modulus Functions `f : R to R,` given by `f (x) =|x|,` is neither one-one nor onto, whre |x| is x, if x is positive or 0 and |x| is -x, if x is negative.

Prove that the function f: R to R, given by f (x) =2x, is one-one and onto.

Show that the function f: R to R given by f (x) = x ^(3) is injective.

Show that the function f: R toR. defined as f (x) =x ^(2), is neither one-one nor onto.

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):}

Show that the function f: N to N, given by f (x) =2x, is one-one but not onto.

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.

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.

Show that the function f given by f(x) = x^(3)-3x^(2)+4x,x in R is increasing on R.

Draw the graph of the function f: R to R defined by f(x)=x^(3), x in R .

Let the function f : R to R be defined by f(x)= 2x + cos x , then f(x)-