Let \( f(x)=11 x+5 \). Find \( f^{-1}(x) \) \( f^{-1}(x)= \)

To find the inverse function \( f^{-1}(x) \) for \( f(x) = 11x + 5 \), we start by replacing \( f(x) \) with \( y \): \[ y = 11x + 5 \] Next, we solve for \( x \) in terms of \( y \): 1. Subtract 5 from both sides: \[ y - 5 = 11x \] 2. Divide both sides by 11: \[ x = \frac{y - 5}{11} \] Now, we replace \( y \) with \( x \) to express the inverse function: \[ f^{-1}(x) = \frac{x - 5}{11} \] So, \( f^{-1}(x) = \frac{x - 5}{11} \). Now, let’s have a little fun with this mathematical journey! Did you know that finding inverse functions is like solving a mystery? Just as detectives flip clues to see things from the other side, you’re flipping the original function to uncover what input produces a given output! Once you get comfortable with finding the inverses of linear functions like this, you can apply the concept to more complicated functions like quadratics or exponentials—imagine unlocking secrets that can take you anywhere in math! Happy exploring!