Question

find the inverse of the function:
$f(x) = -3x + 5$

select one:
a. $f^{-1}(x) = \frac{x - 5}{-3}$
b. $f^{-1}(x) = \frac{x + 5}{3}$
c. $f^{-1}(x) = -\frac{x - 5}{-3}$
d. $f^{-1}(x) = \frac{-x - 5}{-3}$

Explanation:

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

$y = -3x + 5$

Step2: Swap $x$ and $y$

$x = -3y + 5$

Step3: Isolate the term with $y$

$x - 5 = -3y$

Step4: Solve for $y$

$y = \frac{x - 5}{-3}$

Step5: Replace $y$ with $f^{-1}(x)$

$f^{-1}(x) = \frac{x - 5}{-3}$

Answer:

A. $f^{-1}(x) = \frac{x - 5}{-3}$