Question

question
find the inverse function of the function $f(x)=8x - 9$.
answer
$\bigcirc \\ f^{-1}(x)=\frac{x+9}{8}$
$\bigcirc \\ f^{-1}(x)=\frac{x-8}{9}$
$\bigcirc \\ f^{-1}(x)=\frac{x-9}{8}$
$\bigcirc \\ f^{-1}(x)=\frac{x+8}{9}$
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Explanation:

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

$y = 8x - 9$

Step2: Swap $x$ and $y$

$x = 8y - 9$

Step3: Solve for $y$, add 9 to both sides

$x + 9 = 8y$

Step4: Divide both sides by 8

$y = \frac{x+9}{8}$

Step5: Replace $y$ with $f^{-1}(x)$

$f^{-1}(x) = \frac{x+9}{8}$

Answer:

$\boldsymbol{f^{-1}(x) = \frac{x+9}{8}}$ (corresponding to the first option in the answer choices)