Question

Which of the following relation is a one-to-one function?

(a) {(0,0),(1.1),(2,8),(3,27),(4,64)}
(b) {(-2,4),(-1,1),(0,0),(1,1),(2,4)}
(c) {(0,4),(1,5),(2,6),(3,7),..(n,n+4),...}
(d) Height to student

Answer 1

Option (b) {(-2,4),(-1,1),(0,0),(1,1),(2,4)} is the only relation that is a one-to-one function.

Step-by-step explanation:

In order for a relation to be a one-to-one function, each input value must be associated with exactly one output value. Let's analyze the given options:

1. (a) {(0,0),(1.1),(2,8),(3,27),(4,64)}: This relation is not a one-to-one function because the input value 1 is associated with two different output values, 1 and 1.1.
2. (b) {(-2,4),(-1,1),(0,0),(1,1),(2,4)}: This relation is a one-to-one function because each input value is associated with a unique output value.
3. (c) {(0,4),(1,5),(2,6),(3,7),..(n,n+4),...}: This relation is not a one-to-one function because multiple input values are associated with the same output value. For example, both 0 and 1 are associated with the output value 4.
4. (d) Height to student: This option does not provide specific information about input-output associations, so we cannot determine if it is a one-to-one function.

Based on the analysis, option (b) {(-2,4),(-1,1),(0,0),(1,1),(2,4)} is the only relation that is a one-to-one function.