Question

Is the given relation a function? Give reasons for your answer

(i) h = {(4, 6), (3, 9), (– 11, 6), (3, 11)}

(ii) f = {(x, x) | x is a real number}

(iii) g = {(n, 1/n) | n is a positive integer}

(iv) s = {(n, n²) | n is a positive integer}

(v) t = {(x, 3) | x is a real number.

Answer 1

(i) We have, h = {(4,6),(3,9), (-11,6), (3,11)}.

Since pre-image 3 has two images 9 and 11, it is not a function.

(ii) We have, f = {(x, x) | x is a real number}

Since every element in the domain has unique image, it is a function.

(iii) We have, g= {(n, 1/n) | nis a positive integer}

For n, it is a positive integer and 1/n is unique and distinct. Therefore,every element in the domain has unique image. So, it is a function.

(iii) We have, s = {(n, n² ) | n is a positive integer}

Since the square of any positive integer is unique, every element in the domain has unique image. Hence, ibis a function.

(iv) We have, t = {(x, 3)| x is a real number}.

Since every element in the domain has the image 3, it is a constant function.