Question

a function is defined as shown. $f(x) = -3x + 4$ what is the inverse of $f(x)$?

Explanation:

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

$y = -3x + 4$

Step2: Swap $x$ and $y$

$x = -3y + 4$

Step3: Solve for $y$

$3y = 4 - x$
$y = \frac{4 - x}{3}$

Step4: Rename $y$ as $f^{-1}(x)$

$f^{-1}(x) = \frac{4 - x}{3}$

Answer:

$f^{-1}(x) = \frac{4 - x}{3}$