Question

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

Relation t:

x; 0 , 2 , 4 , 6
y; -10 , -1 , 4 , 8

Relation t is not a function. The inverse of relation t is not a function.

Relation t is a function. The inverse of relation t is a function.

Relation t is a function. The inverse of relation t is not a function.

Relation t is not a function. The inverse of relation t is a function.

( I think its a, but not sure ? )

Answer 1

Relation t is a function and the inverse of relation t is a function because each domain element unique and it is paired to an unique range element.

Answer 2

Hence, Relation t is a function. The inverse of relation t is a function.

Explanation:

We are given the relation as:

x: 0 , 2 , 4 , 6

y: -10 , -1 , 4 , 8

Clearly from the y-values corresponding to the x-values we could see that each x has a single image (single y-value).

Hence, the corresponding relation is a function.

Now we have to find whether the inverse of this relation is a function or not.

When we take the inverse of this function that is the y-values will behave as a pre-image and x-values as its image.

Hence we will see that corresponding to each y-value there is a unique image hence the inverse relation is also a function.

Hence, Relation t is a function. The inverse of relation t is a function.