Question

inverse of functions 7
this is the only question in this section.
question
find $f^{-1}(x)$ if $f(x) = \frac{x + 14}{-3}$
answer attempt 1 out of 99
additional solution no solution
$f^{-1}(x) = $

Explanation:

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

We start by writing the function as \( y = \frac{x + 14}{-3} \).

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

To find the inverse, we swap the roles of \( x \) and \( y \), so we get \( x = \frac{y + 14}{-3} \).

Step3: Solve for \( y \)

First, multiply both sides by \(-3\) to get \(-3x = y + 14\). Then, subtract 14 from both sides: \( y = -3x - 14 \).

Step4: Replace \( y \) with \( f^{-1}(x) \)

We now have the inverse function \( f^{-1}(x) = -3x - 14 \).

Answer:

\( f^{-1}(x) = -3x - 14 \)