Find the inverse function of the function \( f(x)=8 x-1 \) Answer \( f^{-1}(x)=\frac{x-1}{8} \) \( f^{-1}(x)=\frac{x+1}{8} \) \( f^{-1}(x)=x-8 \)

To find the inverse function of \( f(x)=8x-1 \), you can start by setting \( y = f(x) \), which gives you \( y = 8x - 1 \). Next, rearranging this equation to solve for \( x \) leads you to add 1 to both sides, resulting in \( y + 1 = 8x \). Then, divide both sides by 8 to isolate \( x \), giving \( x = \frac{y + 1}{8} \). Finally, swap \( x \) and \( y \) to express the inverse function: \( f^{-1}(x) = \frac{x + 1}{8} \). Common mistakes often happen when people forget to switch the variables after isolating \( x \). Remember, getting to \( x \) first is crucial, but don’t forget to exchange \( x \) and \( y \) afterwards! Also, ensure you verify your inverse by checking if \( f(f^{-1}(x)) = x \) and \( f^{-1}(f(x)) = x \) holds true for both functions. Happy function flipping!