Question

what is the domain of the function
$f(x) = 2x - 3$
when the range is ${-9, -3, 1}$?
a. ${-21, -9, -1}$
b. ${-2, 0, 6}$
c. ${-8, -2, 2}$
d. ${-3, 0, 2}$

Explanation:

Step1: Recall the function and range values

The function is \( f(x) = 2x - 3 \), and the range values (outputs of the function) are \(-9\), \(-3\), and \(1\). We need to find the corresponding input values (domain) by setting \( f(x) \) equal to each range value and solving for \( x \).

Step2: Solve for \( x \) when \( f(x) = -9 \)

Set \( 2x - 3 = -9 \).
Add \( 3 \) to both sides: \( 2x = -9 + 3 = -6 \).
Divide by \( 2 \): \( x = \frac{-6}{2} = -3 \).

Step3: Solve for \( x \) when \( f(x) = -3 \)

Set \( 2x - 3 = -3 \).
Add \( 3 \) to both sides: \( 2x = -3 + 3 = 0 \).
Divide by \( 2 \): \( x = \frac{0}{2} = 0 \).

Step4: Solve for \( x \) when \( f(x) = 1 \)

Set \( 2x - 3 = 1 \).
Add \( 3 \) to both sides: \( 2x = 1 + 3 = 4 \).
Divide by \( 2 \): \( x = \frac{4}{2} = 2 \).

Answer:

D. \(\{-3, 0, 2\}\)