Show that the Signum Function `f : R->R ,`given by `f(x)={1,ifx>0 0,ifx=0-1, ifx<0`is neither one-one nor onto.

Show that the Signum Function f : R rarr R given by f(x) = {(1," if " x gt0),(0," if " x =0),(-1," if " x lt0):} is neither one - one nor onto.

Show that the Modulus Function f : R rarr R , given by f(x) = |x| , is neither oneone nor onto , where |x| is x, if x is positive or 0 and |x| is - x , if x is negative.

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

Show that the function given by f(x)=3x+17 is increasing on R.

Let f : R rarr R be the Signum Function defined as f(x) = {(1,xgt0),(0,x = 0),(-1,xlt0):} and g : R rarr R be the Greatest Integer Function given by g(x) = [x] , where [x] is greatest integer less than or equal to x. Then , does fog and gof coincide in (0,1] ?

Show that the function f given by f(x)=tan^(-1)(sin x + cos x), x gt 0 is always an increasing function in (0, (pi)/(4)) .

Show that the function given by f(x)=e^(2x) is increasing on R.

Prove that the function f given by f(x)= |x-1|, x in R is not differentiable at x=1