Question

let $f(x) = 6x + 2$. which of the following is the inverse of $f(x)$?

• $f^{-1}(x) = (x - 2)^6$
• $f^{-1}(x) = \frac{x - 2}{6}$
• $f^{-1}(x) = \frac{x}{6} - 2$
• $f^{-1}(x) = \log_6(x - 2)$
• $f^{-1}(x) = \sqrt6{x - 2}$

Explanation:

Step1: Set $y=f(x)$

$y = 6x + 2$

Step2: Swap $x$ and $y$

$x = 6y + 2$

Step3: Solve for $y$

Subtract 2 from both sides: $x - 2 = 6y$
Divide by 6: $y = \frac{x-2}{6}$

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

$f^{-1}(x) = \frac{x-2}{6}$

Answer:

$\boldsymbol{f^{-1}(x)=\frac{x-2}{6}}$ (the second option)