Question

given $g(x)=\frac{(3x + 5)}{2}$, which of the following shows that creating the equation of the inverse means switching the variables and solving for $y$? (1 point)
$y=\frac{2}{3}(x - 5)$
$y=\frac{1}{3}(2x - 5)$
$y=\frac{(3x - 5)}{2}$
$y=\frac{(2x + 5)}{3}$

Explanation:

Step1: Let \(y = g(x)\)

\(y=\frac{3x + 5}{2}\)

Step2: Switch \(x\) and \(y\)

\(x=\frac{3y + 5}{2}\)

Step3: Solve for \(y\)

First, multiply both sides by 2: \(2x=3y + 5\). Then subtract 5 from both sides: \(2x-5 = 3y\). Finally, divide both sides by 3: \(y=\frac{1}{3}(2x - 5)\)

Answer:

\(y=\frac{1}{3}(2x - 5)\) (corresponding to the second - option in the multiple - choice list)