Give an example of a function which is
`"(i) one-one but not onto " " " "(ii) one-one and onto"`
`(iii) "neither one-one nor onto" " " "(iv) onto but not one-one"`

Give an example of a function which is one-one but not onto.which is not one-one but onto. (iii) which is neither one-one nor 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

f: R rarr R,f(x)=x|x| is (A) one-one but not onto (B) onto but not one-one (C) Both one-one and onto (D) neither one-one nor onto

Let M be the set of all 2xx2 matrices with entries from the set R of real numbers. Then the function f: M->R defined by f(A)=|A| for every A in M , is (a) one-one and onto (b) neither one-one nor onto (c) one-one but not onto (d) onto but not one-one

A function f from the set of natural numbers to integers is defined by n when n is odd f(n)3, when n is even Then f is (b) one-one but not onto a) neither one-one nor onto (c) onto but not one-one (d) one-one and onto both

If the functions f(x)a n dg(x) are defined on R rarr R such that f(x)={0, x in r a t ion a l x ,x in i r r a t ion a l a n dg(x)={O , x in i r r a t ion a l x ,x in r a t ion a l then (f-g)(x)i s (a)one-one and onto (b)neither one-one nor onto (c)one-one but not onto (d)onto but not one-one

81. A mapping f:R rarr R R which is defined as f(x)=cos x;x in R is: (a) oniy one-one (b) only onto (C) one-one onto (d) Neither one-one nor onto

If a function f:[2,\ oo)->R defined by f(x)=(x-1)(x-2)(x-3) is (a) one-one but not onto (b) onto but not one-one (c) both one and onto (d) neither one-one nor onto

f: R->R is defined by f(x)=(e^x^2-e^-x^2)/(e^x^2+e^-x^2) is (a) one-one but not onto (b) many-one but onto (c) one-one and onto (d) neither one-one nor onto

The function f:[0,\ oo)->R given by f(x)=x/(x+1) is (a) one-one and onto (b) one-one but not onto (c) onto but not one-one (d) neither one-one nor onto