Let `f : A rarr B, g : B rarr C` be two functions such that gof is one-one and onto. Show that f is one-one and g is onto.

Show that the function f(x)=3x+2 is one-one and onto.

Give an example of a function which is one one but not onto

Let f : R rarr R, f(x)=x^2 and g : R rarr R,g(x)=sinx be two given functions. Is gof=fog ?

Let f:R toR and g:R to R be two functions given by f(x)=cosx and g(x)=3x^(2) . Show that gof!=fog .

Give an example of a function which is neither one - one nor onto

A function f:R to R is defined by f(x)=4x^(3)+5x in R . Examine if f is one - one and onto.

Give an example to show that the function gof is defined and onto though the functions both f and g are not necessarily onto.

Give an example of a function which is onto but not one - one.