Answer:
Relation t is a function. The inverse of relation t is not a function ⇒ 3rd
Explanation:
* Lets explain how to solve the problem
- A relation is a set of inputs and outputs, and a function is a relation
with one output for each input
- Ex: T = {(1 , 2) , (3 , 5) , (-4 , 0)} is a function because every input has
only one output
- To find the inverse of a function we switched the input and the
out put
- The inverse of a function may not always be a function
* Lets solve the problem
∵ The relation t is the set of ordered pairs of x and y
x = 0 2 4 6
y = -8 -7 -4 -4
∵ x = 0 has only y = -8
∵ x = 2 has only y = -7
∵ x = 4 has only y = -4
∵ x = 6 has only y = -4
∴ Every value of x has only one value of y
∴ Relation t is a function
* Lets find its inverse by switching x and y
∵ The inverse function of t is :
x = -8 -7 -4 -4
y = 0 2 4 6
∵ x = -8 has only y = 0
∵ x = -7 has only y = 2
∵ x = -4 has y = 4 and y = 6
∴ Not every value of x has only one value of y
∴ The inverse of relation t is not a function
* Relation t is a function. The inverse of relation t is not a function