Question

inverse of functions 8
this is the only question in this section.
question
find $f^{-1}(x)$ if $f(x) = \frac{x - 15}{-8}$
answer attempt 1 out of 99
additional solution no solution
$f^{-1}(x) = \square$
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Explanation:

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

We start by writing the function as \( y = \frac{x - 15}{-8} \).

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

To find the inverse, we interchange \( x \) and \( y \), so we get \( x = \frac{y - 15}{-8} \).

Step3: Solve for \( y \)

First, multiply both sides by \(-8\) to get rid of the denominator: \( -8x = y - 15 \).
Then, add \( 15 \) to both sides to solve for \( y \): \( y = -8x + 15 \).

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

We now have the inverse function \( f^{-1}(x) = -8x + 15 \).

Answer:

\( f^{-1}(x) = -8x + 15 \)