If the given relation a fucntion? Give reason for your answer.
(i) `h={(4,6),(3,9),(-11,6),(3,11)}`
(ii) `f={(x,x)|x` is a real number }
(iii) `g={(x,(1)/(x))x` is a positive integer}
(iv) `s={(x,x^(2))|x` is positive integer}
(v) t={(x,3)|x is a real number}

Explanation

We haveh=`{(4,6),(3,9),(-11,6),(3,11)}`
Since, 3 has two image 9 to 11 . So, it is not a function.
(ii) We have f={(x ,x)|x is a real number
We observe, that, every element in the domain has unique image . So it is function.
(iii) We have, `g={(x,(1)/(x))x` is a positive integer}
For every x, it is a positive integer and `(1)/(x)` is unique and distinct. Therefore, every element in the domain has unique . So it is a function.
We have `s={x,x^(2))|x` is a positive integer }
Since, the square of any positive integer is unique. So every element in the domain has unique image. Hence it a a function.
We have `t={(x,3)|x` is a real number}
Since, every element in the domain has the image 3. so it is a constant function.