Prove that the function `f: N rarr N` , defined by
`f(x)=x^2+x+1` is one-one but not onto.

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

Show that the function f : R_** rarr R_** defined by f (x) = 1/x is one-one and onto,where R_** is the set of all non-zero real numbers. Is the result true, if the domain R_** is replaced by N with co-domain being same as R_** ?

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

Prove that the function defined by f(x)= cosx^2 is a continuous function

Let A = R - {-3} and B = R - {1} Consider the function f : A rarr B defined by f(x) = (x-2)/(x-3) . Is f one-one and onto ? Justify your answer.

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

Show that the function f:RtoR defined by f(x)=2x-3 is one-one and onto. Find f^-1

A fuction f:RrarrR defined by f(x)=(2x-3)/7 .Is f a one-one function?Why?

Show that the function f in A=R-{2/3} defined as f(x)=(4x+3)/(6x-4) is one-one and onto.