Let `f: A->A` be a function such that `fof=f` . Show that `f` is onto if and only if `f` is one-one. Describe `f` in this case.

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

Let f:R to R where f(x) =sin x. Show that f is into. Also find the codomain if f is onto.

Using the definition, Prove that the function f:A to B is invertible if and only if f is both one-one and onto.

Show that the function f:N rarr N given by f(x)=3x is one one but not onto

If f is a function from RrarrR such that f(x)=x^(2)AA x inR , then show that 'f' is not one-one.

Let f: R-{n}->R be a function defined by f(x)=(x-m)/(x-n) such that m!=n 1) f is one one into function2) f is one one onto function3) f is many one into funciton4) f is many one onto funcionn then

Show that the function f:N rarr N, given by f(x)=2x, is one-one but not onto.

Let f:A rarr B and g:B rarr C be two functions.Then; if gof is onto then g is onto; if gof is one one then f is one-one and if gof is onto and g is one one then f is onto and if gof is one one and f is onto then g is one one.

Show that the function f:R rarr R:f(x)=sin x is neither one-one nor onto

If functions f:A to B and g : B to A satisfy gof= I_(A), then show that f is one-one and g is onto.