Question

What is domain of the function y=3x-4 when the range is {-7,2,8,14}?

Answer 1

The domain of the function
`y = 3\cdot x - 4` is
`Dom \{f\} = \{-1,2,4,6\}`.

Explanation:

The domain of a given function is the set of values of
`x` such that respective elements of the range, represented by the set of values of
`y`, exist. Then, we must clear
`x` within the given function:

1)
`y = 3\cdot x - 4` Given

2)
`y +4 = 3\cdot x` Compatibility with addition/Existence of additive inverse/Modulative property

3)
`x = (y+4)/(3)` Compatibility with multiplication/Associative property/Existence of multiplicative inverse/Modulative property/Symmetrical property of equalities/Result

Now, we obtain the set of elements of the domain:

y = -7

`x = (-7+4)/(3)`

`x = -1`

y = 2

`x = (2+4)/(3)`

`x = 2`

y = 8

`x = (8+4)/(3)`

`x = 4`

y = 14

`x = (14+4)/(3)`

`x = 6`

The domain of the function
`y = 3\cdot x - 4` is
`Dom \{f\} = \{-1,2,4,6\}`.