Question

a function is defined as shown.$f(x) = -3x + 4$what is the inverse of $f(x)$?a. $f^{-1}(x) = -\frac{1}{3}x - 4$b. $f^{-1}(x) = -\frac{1}{3}x + \frac{4}{3}$c. $f^{-1}(x) = -\frac{1}{3}x + 4$d. $f^{-1}(x) = \frac{1}{3}x - \frac{4}{3}$

Explanation:

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

$y = -3x + 4$

Step2: Swap $x$ and $y$

$x = -3y + 4$

Step3: Solve for $y$

Subtract 4 from both sides: $x - 4 = -3y$
Divide by -3: $y = -\frac{1}{3}x + \frac{4}{3}$

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

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

Answer:

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