Show that the function `f : R rarr R` defined by `f(x)=[x]`, where `[x]` is the greatest integer less than equal to x is neither one-one nor onto.

Show that the function f : R rarr R defined by f(x)=x^2+4 is not invertible.

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

Show that the function f : R_0 rarr R_0 defined by f(x)=1/x , where R_0 is the set of nonzero real numbers is bijective.

Show that the function f : R rarr R , defined by {(-1,x 0):} is neither one-one nor onto.

Show that the function f: R to R defined by f(x)=2x^(2) , is neither one - one onto.

Sketch the graph of the function f given by f(x)=[x], where [ x ] is the Greatest integer function of x.

Let f:R to R and g: R to R be two functions defined by f(x)=|x|" and "g(x)=[x] , where [x] denotes the greatest integer less than or equal to x. Find (fog) (5.75) and (gof)(-sqrt(5)) .

If f : R rarr R be defined by f(x)=|x| , show that fof=f

Prove that the function f:N rarr N defined by f(x)=x^2+2 is one-one but not onto.