Show that a one-one function `f : {1, 2, 3}-> {1, 2, 3}`must be onto.

Show that an onto function f" ":" "{1," "2," "3} ->{1," "2," "3} is always one-one.

If the function f : { 1,2,3} rarr { 1,2,3} is one one then it must be :

If A={1,2,3}, show that an onto function f:A rarr A must be one-one

Show that the function f : R to R : f(x) =3-4 x is one-one onto and hence bijective.

Let f" ":" "{1," "2," "3}->{a ," "b ," "c} be one-one and onto function given by f" "(1)" "=" "a , f" "(2)" "=" "b and f" "(3)" "=" "c . Show that there exists a function g" ":" "{a ," "b ," "c}->{1," "2," "3} such that gof=I_x and fog=

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

bijective llUll (iii) full (v) into function functions. Give an example of each type of 3. Give an example of a function which is (ii) one-one and (i) one-one but not onto (iv) onto but not o (iii) neither one-one nor onto 4. Let f: R R be defined by 2x 3, when x <-2 3x2 2, when -2 s x s 3 f(x) 3x -1, when x 3. IV 5. Show that the function f R R: for 1 6. Show that the function f R R: x) x is many-C 7. Show that the function f R R: f(x) x is many-one a Let f 0 R f (x) sin x and X is one-one ano Sweet Self ie

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

show that the function f : R to R f : (x) = x^(5) is one-one and onto .

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