Show that the function `f:RrarrR` given by `f(x)=x+x^3`is a bijective function.

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

The function f:NtoN given by f(x)=2x

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(x) defined by f(x)=sin(cosx) is a continuous function .

Show that the function given by f(x)=7 x-3 is strictly increasing on R

Show that the function defined by f(x)=sin (x^2) is a continuous function.

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

Show that the function given by f(x)=(logx)/x has maximum at x = e

Prove that the function f: Q rarr Q given by f(x)=2 x-3 for all x in Q (the set of all rational numbers) is a bijection.