Question

find the inverse function of the function $f(x)=3x-7$.
answer
$\bigcirc$ $f^{-1}(x)=\frac{x+7}{3}$
$\bigcirc$ $f^{-1}(x)=3x+7$
$\bigcirc$ $f^{-1}(x)=\frac{x-7}{3}$
$\bigcirc$ $f^{-1}(x)=\frac{1}{3}x-7$
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Explanation:

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

$y = 3x - 7$

Step2: Swap $x$ and $y$

$x = 3y - 7$

Step3: Solve for $y$, add 7 to both sides

$x + 7 = 3y$

Step4: Isolate $y$, divide by 3

$y = \frac{x+7}{3}$

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

$f^{-1}(x) = \frac{x+7}{3}$

Answer:

$f^{-1}(x) = \frac{x+7}{3}$