Chapter 1.7, Problem 3ACYP

To determine

To find:

If the given relation $4x=8$ or $0y+x=\frac{8}{4}=2$ , is a function.

Answer to Problem 3ACYP

No, given relation is not a function because for two same input values (i.e. 2), there is always a different output value.

Explanation of Solution

Given information:

Given a relation, $4x=8$ .

Concept used:

A relation is a function,

• If for each value in its domain; there is always a unique value in its co domain.
• If for each different first value of its ordered pair, there is always a second unique value, then such relation is a function always.
• Or, no two same first values, should have two different second values in ordered pairs of set of relation.

Calculation:

Given relation can also be simplified as $0y+4x=8$ , so its relation as a set of ordered pairs can be set as:

  $R=\{\left(2,0\right),\left(2,1\right),\left(2,3\right)\dots .\}$

So, for any two same first values, there is a different second value in ordered pairs that means the values of domain are not associated with a unique value of its co domain.

Conclusion:

In above relation, for same first values in ordered pairs, there are different second values. Or two same input values, have different output that is against the definition of a function. So, this relation is not a function.