Question

find the inverse of the function. f(x) = x - 9 write your answer in the form ax + b. simplify any fractions. f⁻¹(x) =

Explanation:

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

We start by writing the function as \( y = x - 9 \).

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

To find the inverse, we interchange \( x \) and \( y \), so we get \( x = y - 9 \).

Step3: Solve for \( y \)

We add 9 to both sides of the equation to isolate \( y \). So, \( y = x + 9 \).

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

Now we replace \( y \) with the inverse function notation, giving \( f^{-1}(x)=x + 9 \).

Answer:

\( f^{-1}(x)=x + 9 \)