Question

1. which is the inverse of the function $f(x) = 4x - 9$?

$y = \frac{x - 9}{4}$
$y = 4(x + 9)$
$y = \frac{x + 9}{4}$
$y = \frac{x}{4} + 9$

Explanation:

Step1: Replace $f(x)$ with $y$

We start with the function $f(x)=4x - 9$. Replace $f(x)$ with $y$, so we have $y = 4x-9$.

Step2: Swap $x$ and $y$

To find the inverse, we swap the roles of $x$ and $y$. This gives us $x = 4y-9$.

Step3: Solve for $y$

First, add 9 to both sides of the equation: $x + 9=4y$. Then, divide both sides by 4: $y=\frac{x + 9}{4}$.

Answer:

$y = \frac{x + 9}{4}$ (the third option, with the boxed formula $y=\frac{x + 9}{4}$)