Question

find the inverse function of the function $f(x) = 6x + 7$.
answer
$\bigcirc$ $f^{-1}(x) = \frac{x-7}{6}$
$\bigcirc$ $f^{-1}(x) = \frac{x+7}{6}$
$\bigcirc$ $f^{-1}(x) = \frac{1}{6}x + 7$
$\bigcirc$ $f^{-1}(x) = 6x - 7$

Explanation:

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

$y = 6x + 7$

Step2: Swap $x$ and $y$

$x = 6y + 7$

Step3: Isolate the term with $y$

$x - 7 = 6y$

Step4: Solve for $y$

$y = \frac{x - 7}{6}$

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

$f^{-1}(x) = \frac{x - 7}{6}$

Answer:

A. $f^{-1}(x) = \frac{x-7}{6}$