Q. 18

# Given A = {2, 3, 4}, B = {2, 5, 6, 7}. Construct an example of each of the following:

(a) an injective mapping from A to B

(b) a mapping from A to B which is not injective

(c) a mapping from B to A.

Answer :

Given that, A = {2, 3, 4}, B = {2, 5, 6, 7}

(a) an injective mapping from A to B

Let f : A → B denote a mapping f = {(x,y) : y=2x }

Now, y = 2x

When x=2 we get y = 4

Similarly, x=3 and 4 will give y=6 and 8 respectively.

∴ f = {(2,4),(3,6),(4,8)}

We observe that each element of A has unique image in B.

Thus, f is injective.

(b) a mapping from A to B which is not injective

Let g: A → B denote a mapping such that g = {(2,2),(3,5),(4,2)}

We observe that 2 and 4 ∈ A does not have unique image.

Thus, g is not injective.

(c) a mapping from B to A.

Let h : B → A denote a mapping such that

h = {(2,3),(5,2),(6,3),(7,4)}

Rate this question :

Fill in the blanks in each of the

Let f :R → R be defined by. Then (f o f o f) (x) = _______

Mathematics - ExemplarLet f : [2, ∞) → R be the function defined by f (x) = x^{2}–4x+5, then the range of f is

Let f : N → R be the function defined byand g : Q → R be another function defined by g (x) = x + 2. Then (g o f)3/2 is

Mathematics - ExemplarFill in the blanks in each of the

Let f = {(1, 2), (3, 5), (4, 1) and g = {(2, 3), (5, 1), (1, 3)}. Then g o f = ______and f o g = ______.

Mathematics - ExemplarLet f :R → R be defined by

Then f (– 1) + f (2) + f (4) is

Mathematics - ExemplarLet f : [0, 1] → [0, 1] be defined by

Then (f o f) x is

Mathematics - ExemplarWhich of the following functions from Z into Z are bijections?

Mathematics - Exemplar