Which of the following relations are functions? Give reasons. If it is a function, determine its domain and range. (i) {(2, 1), (5, 1), (8, 1), (11, 1), (14, 1), (17, 1)} (ii) {(2, 1), (4, 2), (6, 3), (8, 4), (10, 5), (12, 6), (14, 7)} (iii) {(1, 3), (1, 5), (2, 5)}

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Solution

(i)

The given relation is,

{ ( 2,1 ),( 5,1 ),( 8,1 ),( 11,1 ),( 14,1 ),( 17,1 ) }.

Since the elements of domain 2,5,8,11,14,17 have their unique images, so, the given relation is a function.

The domain of the given relation is,

{ 2,5,8,11,14,17 }

The range of the given relation is,

{ 1 }

(ii)

The given relation is,

{ ( 2,1 ),( 4,2 ),( 6,3 ),( 8,4 ),( 10,5 ),( 12,6 ),( 14,7 ) }.

Since the elements of domain 2,4,6,8,10,12,14 have their unique images, so, the given relation is a function.

The domain of the given relation is,

{ 2,4,6,8,10,12,14 }

The range of the given relation is,

{ 1,2,3,4,5,6,7 }

(iii)

The given relation is,

{ ( 1,3 ),( 1,5 ),( 2,5 ) }

Since the first element of domain has two different images, so the given relation is not a function.

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Similar questions

{(2, 1), (5, 1), (8, 1), (11, 1), (14, 1), (17, 1)}

{(2, 1), (4, 2), (6, 3), (8, 4), (10, 5), (12, 6), (14, 7)}

{(1, 3), (1, 5), (2, 5)}

(i) {(2, 1), (5, 1), (8, 1), (11, 1) (14, 1), (17, 1)}

(i i) {(2, 1), (4, 2), (6, 3), (8, 4) (10, 5), (12, 6), (14, 7)}

(i i i) {(1, 3), (1, 5), (2, 5)}

Which of the following relations are functions? Give reasons. If it is a function determine its domain and range.

(i) {(2, 1), (5, 1), (8, 1), (11, 1), (14, 1), (17, 1)}

(ii) {(2, 1), (4, 2), (6, 3), (8, 4), (10, 5), (12, 6), (14, 7)}

(iii) {(1, 3), (1, 5), (2, 5)}

Which of the following is not correct about the function f(x)=0?

f (x) = a^{x} \forall ϵ R

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