Q. 125.0( 3 Votes )

# Let X = {1, 2, 3} and Y = {4, 5}. Find whether the following subsets of X × Y are functions from X to Y or not.

(i) f = {(1, 4), (1, 5), (2, 4), (3, 5)}

(ii) g = {(1, 4), (2, 4), (3, 4)}

(iii) h = {(1,4), (2, 5), (3, 5)}

(iv) k = {(1,4), (2, 5)}.

Answer :

We have,

X = {1, 2, 3} and Y = {4, 5}

∴ X × Y = {(1, 4),(1, 5),(2, 4),(2, 5),(3, 4),(3, 5)}

(i) f = {(1, 4), (1, 5), (2, 4), (3, 5)}

Now, f(1) = 4 and f(1) = 5

We observe that one element of domain maps to two distinct values.

i.e., ‘1’ has no unique image.

Thus, f is not a function.

(ii) g = {(1, 4), (2, 4), (3, 4)}

Now, g(1) = 4, g(2) = 4, g(3) = 4

We observe that each distinct element of domain has unique image.

Thus, g is a function.

(iii) h = {(1,4), (2, 5), (3, 5)}

Now, h(1) = 4, h(2) = 5, h(3) = 5

We observe that each distinct element of domain has unique image.

Thus, h is a function.

(iv) k = {(1,4), (2, 5)}.

Now, k(1) = 4 and k(2) = 5

We observe that ‘3’ does not have any image under the mapping.

Thus, k is not a function.

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