Question

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

Answer 1

Answer:

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

Step-by-step 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) $x = \frac{y+4}{3}$ 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

$x = \frac{-7+4}{3}$

$x = -1$

y = 2

$x = \frac{2+4}{3}$

$x = 2$

y = 8

$x = \frac{8+4}{3}$

$x = 4$

y = 14

$x = \frac{14+4}{3}$

$x = 6$

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