Question

question 13.
let (f(x) = \frac{1}{x + 8}).
(f^{-1}(x) = \frac{1}{x} - 8)

Explanation:

⚡ Using what you learned: inverse functions: definition and notation

Step 1: Replace \( f(x) \) with \( y \)

$$ y = \frac{1}{x + 8} $$

Step 2: Swap \( x \) and \( y \)

$$ x = \frac{1}{y + 8} $$

Step 3: Solve for \( y \)

$$ y + 8 = \frac{1}{x} $$

$$ y = \frac{1}{x} - 8 $$

Step 4: Replace \( y \) with \( f^{-1}(x) \)

$$ f^{-1}(x) = \frac{1}{x} - 8 $$

Answer:

$$ f^{-1}(x) = \frac{1}{x} - 8 $$