Question

In relation t a functions? Is the inverse of relation t function

Answer 1

Answer:

Relation t is a function. The inverse of relation t is not a function ⇒ 3rd

Step-by-step 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